Shub, Michael 1943
Overview
Works:  66 works in 184 publications in 3 languages and 2,015 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other 
Classifications:  QA76, 514 
Publication Timeline
.
Most widely held works by
Michael Shub
Global stability of dynamical systems by
Michael Shub(
Book
)
36 editions published between 1978 and 1987 in 3 languages and held by 552 WorldCat member libraries worldwide
These notes are the result of a course in dynamical systems given at Orsay during the 197677 academic year. I had given a similar course at the Gradu ate Center of the City University of New York the previous year and came to France equipped with the class notes of two of my students there, Carol Hurwitz and Michael Maller. My goal was to present Smale's nStability Theorem as completely and compactly as possible and in such a way that the students would have easy access to the literature. I was not confident that I could do all this in lectures in French, so I decided to distribute lecture notes. I wrote these notes in English and Remi Langevin translated them into French. His work involved much more than translation. He consistently corrected for style, clarity, and accuracy. Albert Fathi got involved in reading the manuscript. His role quickly expanded to extensive rewriting and writing. Fathi wrote (5. 1) and (5. 2) and rewrote Theorem 7. 8 when I was in despair of ever getting it right with all the details. He kept me honest at all points and played a large role in the final form of the manuscript. He also did the main work in getting the manuscript ready when I had left France and Langevin was unfortunately unavailable. I ran out of steam by the time it came to Chapter 10. M
36 editions published between 1978 and 1987 in 3 languages and held by 552 WorldCat member libraries worldwide
These notes are the result of a course in dynamical systems given at Orsay during the 197677 academic year. I had given a similar course at the Gradu ate Center of the City University of New York the previous year and came to France equipped with the class notes of two of my students there, Carol Hurwitz and Michael Maller. My goal was to present Smale's nStability Theorem as completely and compactly as possible and in such a way that the students would have easy access to the literature. I was not confident that I could do all this in lectures in French, so I decided to distribute lecture notes. I wrote these notes in English and Remi Langevin translated them into French. His work involved much more than translation. He consistently corrected for style, clarity, and accuracy. Albert Fathi got involved in reading the manuscript. His role quickly expanded to extensive rewriting and writing. Fathi wrote (5. 1) and (5. 2) and rewrote Theorem 7. 8 when I was in despair of ever getting it right with all the details. He kept me honest at all points and played a large role in the final form of the manuscript. He also did the main work in getting the manuscript ready when I had left France and Langevin was unfortunately unavailable. I ran out of steam by the time it came to Chapter 10. M
Invariant manifolds by
Morris W Hirsch(
Book
)
20 editions published in 1977 in 3 languages and held by 408 WorldCat member libraries worldwide
20 editions published in 1977 in 3 languages and held by 408 WorldCat member libraries worldwide
The mathematics of numerical analysis : 1995 AMSSIAM Summer Seminar in Applied Mathematics, July 17August 11, 1995, Park
City, Utah by AMSSIAM Summer Seminar in Applied Mathematics(
Book
)
9 editions published between 1995 and 1996 in English and held by 229 WorldCat member libraries worldwide
9 editions published between 1995 and 1996 in English and held by 229 WorldCat member libraries worldwide
From topology to computation : proceedings of the Smalefest by
Morris W Hirsch(
Book
)
15 editions published between 1990 and 1993 in English and held by 180 WorldCat member libraries worldwide
This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging over a wide variety of fields in pure and applied mathematics. In addition, Smale has provided an autobiographical essay, as well as a record of the lively panel discussions at the symposium. The research contributions include papers on differential topology, mathematical economics, dynamical systems, on the theory of computation, on nonlinear functional analysis, and on various applications in the physical and biological sciences. All are currently active areas of interdisciplinary research
15 editions published between 1990 and 1993 in English and held by 180 WorldCat member libraries worldwide
This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging over a wide variety of fields in pure and applied mathematics. In addition, Smale has provided an autobiographical essay, as well as a record of the lively panel discussions at the symposium. The research contributions include papers on differential topology, mathematical economics, dynamical systems, on the theory of computation, on nonlinear functional analysis, and on various applications in the physical and biological sciences. All are currently active areas of interdisciplinary research
Foundations of computational mathematics : selected papers of a conference held at Rio de Janeiro, January 1997 by
Felipe Cucker(
Book
)
13 editions published in 1997 in English and German and held by 145 WorldCat member libraries worldwide
This book contains articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics (FoCM) conference at IMPA in Rio de Janeiro in January 1997. FoCM brings together a novel constellation of subjects in which the computational process itself and the foundational mathematical underpinnings of algorithms are the objects of study. The conference was organized around nine workshops: systems of algebraic equations and computational algebraic geometry, homotopy methods and real machines, information based complexity, numerical linear algebra, approximation and PDE's, optimization, differential equations and dynamical systems, relations to computer science and vision and related computational tools. The book gives the reader an idea of the state of the art in this emerging discipline
13 editions published in 1997 in English and German and held by 145 WorldCat member libraries worldwide
This book contains articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics (FoCM) conference at IMPA in Rio de Janeiro in January 1997. FoCM brings together a novel constellation of subjects in which the computational process itself and the foundational mathematical underpinnings of algorithms are the objects of study. The conference was organized around nine workshops: systems of algebraic equations and computational algebraic geometry, homotopy methods and real machines, information based complexity, numerical linear algebra, approximation and PDE's, optimization, differential equations and dynamical systems, relations to computer science and vision and related computational tools. The book gives the reader an idea of the state of the art in this emerging discipline
Stably ergodic approximation : two examples by
Michael Shub(
Book
)
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "It has been conjectured that the stably ergodic diffeomorphisms are open and dense in the space of volumepreserving, partiallyhyperbolic diffeomorphisms of a compact manifold. In this paper we deal with two recalcitrant examples; the standard map cross Anosov and the ergodic automorphisms of the four torus. In both cases we show that they may be approximated by stably ergodic diffeomorphisms which have the stable accessibility property."
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "It has been conjectured that the stably ergodic diffeomorphisms are open and dense in the space of volumepreserving, partiallyhyperbolic diffeomorphisms of a compact manifold. In this paper we deal with two recalcitrant examples; the standard map cross Anosov and the ergodic automorphisms of the four torus. In both cases we show that they may be approximated by stably ergodic diffeomorphisms which have the stable accessibility property."
A stably Bernoullian diffeomorphism that is not Anosov by
Michael Shub(
Book
)
2 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Newton and predictorcorrector methods for overdetermined systems of equations by J. P Dedieu(
Book
)
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "Complexity theoretic aspects of continuation methods for the solution of square or underdetermined systems of polynomial equations have been studied by various authors. In this paper we consider overdetermined systems where there are more equations than unknowns. We take two approaches to the problem. In the first we study Newton's method for an overdetermined system and then apply it to the elements of a path in the space of problems to produce a path of solutions. In the second we study the map from the variety of solutions to the variety of problems and use its structure to lift a path of problems to solutions. We call these second methods predictorcorrector methods."
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "Complexity theoretic aspects of continuation methods for the solution of square or underdetermined systems of polynomial equations have been studied by various authors. In this paper we consider overdetermined systems where there are more equations than unknowns. We take two approaches to the problem. In the first we study Newton's method for an overdetermined system and then apply it to the elements of a path in the space of problems to produce a path of solutions. In the second we study the map from the variety of solutions to the variety of problems and use its structure to lift a path of problems to solutions. We call these second methods predictorcorrector methods."
Stable ergodicity and julienne quasiconformality by Charles Pugh(
Book
)
2 editions published in 1997 in English and held by 6 WorldCat member libraries worldwide
Abstract: "In this paper we eliminate some of the most nettlesome hypotheses of our previous article, 'Stably ergodic dynamical systems and partial hyperbolicity' [22], and expand the domain of stably ergodic, partially hyperbolic dynamical systems to include all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property. Our main tool is a new concept  julienne quasi conformality of the stable and unstable holonomy maps. An important feature of this is that the holonomy maps preserve all julienne density points."
2 editions published in 1997 in English and held by 6 WorldCat member libraries worldwide
Abstract: "In this paper we eliminate some of the most nettlesome hypotheses of our previous article, 'Stably ergodic dynamical systems and partial hyperbolicity' [22], and expand the domain of stably ergodic, partially hyperbolic dynamical systems to include all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property. Our main tool is a new concept  julienne quasi conformality of the stable and unstable holonomy maps. An important feature of this is that the holonomy maps preserve all julienne density points."
Stable ergodicity and stable accessibility by
Cedric D. J Pugh(
Book
)
2 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
Abstract: "In this paper we discuss how a little hyperbolicity goes a long way towards guaranteeing stable ergodicity. Examples to which our theory applies include translations on certain homogeneous spaces and the time one map of the geodesic flow for a manifold of constant negative curvature. We also discuss the role played by a concept from control theory, accessibility by paths tangent to a pair of subbundles of the tangent bundle."
2 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
Abstract: "In this paper we discuss how a little hyperbolicity goes a long way towards guaranteeing stable ergodicity. Examples to which our theory applies include translations on certain homogeneous spaces and the time one map of the geodesic flow for a manifold of constant negative curvature. We also discuss the role played by a concept from control theory, accessibility by paths tangent to a pair of subbundles of the tangent bundle."
On simple double zeros and badly conditioned zeros of analytic functions of n variables by JeanPierre Dedieu(
Book
)
3 editions published in 1999 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1999 in English and held by 5 WorldCat member libraries worldwide
The identity is best for 2 x 2 real matrices by
Debra J Lewis(
Book
)
2 editions published in 1999 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 5 WorldCat member libraries worldwide
On a theory of computation and complexity over the real numbers : NP completeness, recursive functions and universal machines by
Lenore Blum(
Book
)
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
Publications mathematiques de l'i.h.e.s by France) Institut des hautes études scientifiques (Paris(
Book
)
1 edition published in 1979 in French and held by 4 WorldCat member libraries worldwide
1 edition published in 1979 in French and held by 4 WorldCat member libraries worldwide
Endomorphisms of compact differentiable manifolds by
Michael Shub(
)
2 editions published in 1967 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1967 in English and held by 4 WorldCat member libraries worldwide
Stable ergodicity in homogeneous spaces by
Jonathan Brezin(
Book
)
1 edition published in 1995 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 4 WorldCat member libraries worldwide
Can one always lower topological entropy by
Michael Shub(
Book
)
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
On the work of Steve Smale on the theory of computation by
Michael Shub(
Book
)
3 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
How many eigenvalues of a random matrix are real? by
Alison Edelman(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Complexity and real computation by
Lenore Blum(
Book
)
4 editions published between 1984 and 1998 in English and held by 1 WorldCat member library worldwide
The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NPcompleteness theorems of CookKarp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing
4 editions published between 1984 and 1998 in English and held by 1 WorldCat member library worldwide
The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NPcompleteness theorems of CookKarp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Hirsch, Morris W. 1933 Author Editor
 Pugh, C. C. (Charles Chapman) 1940
 Smale, Stephen 1930 Other Author
 Fathi, Albert Other Editor
 Langevin, Remi Other Editor
 Cucker, Felipe 1958 Author Editor
 Renegar, James 1955 Other Editor
 Marsden, Jerrold E. Editor
 Blum, Lenore Author
 SpringerLink (Service en ligne)
Useful Links
Associated Subjects
Algebra Bernoulli shifts Cell aggregationMathematics Computational complexity Computer algorithms Computer science Computer software Continuation methods Determinants Differentiable dynamical systems Differential equations Differential topology Eigenvalues EigenvaluesComputer programs Ergodic theory Exponential functions Foliations (Mathematics) Geometry Geometry, Differential Global analysis (Mathematics) Hermitian operators Homogeneous spaces Homology theory Information theory Invariant manifolds Invariants Logic, Symbolic and mathematical Manifolds (Mathematics) Mappings (Mathematics) Mathematics MathematicsData processing Matrices Morphisms (Mathematics) NewtonRaphson method NPcomplete problems Number theory Numerical analysis Numerical calculations Polynomials Programming (Mathematics) Random matrices Realtime data processing Riemannian manifolds Singularities (Mathematics) Stability Submanifolds Topological dynamics Topology
Alternative Names
Michael Shub American mathematician
Michael Shub Amerikaans wiskundige
Michael Shub USamerikanischer Mathematiker
Shub, M.
Shub, M. 1943
Shub, M. (Michael), 1943
Shub, Michael
Shub, Michael 1942
Shub, Michael Ira
Shub, Michael Ira 1943
Shub, Mike
Languages
Covers