Shub, Michael 1943
Overview
Works:  71 works in 162 publications in 3 languages and 1,776 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor 
Classifications:  QA76, 511.3 
Publication Timeline
.
Most widely held works by
Michael Shub
Invariant manifolds
by
Morris W Hirsch(
Book
)
17 editions published in 1977 in English and German and held by 515 WorldCat member libraries worldwide
17 editions published in 1977 in English and German and held by 515 WorldCat member libraries worldwide
Global stability of dynamical systems
by
Michael Shub(
Book
)
15 editions published between 1986 and 1987 in English and held by 393 WorldCat member libraries worldwide
15 editions published between 1986 and 1987 in English and held by 393 WorldCat member libraries worldwide
The mathematics of numerical analysis : 1995 AMSSIAM Summer Seminar in Applied Mathematics, July 17August 11, 1995, Park City, Utah
by Summer Seminar on Applied Mathematics(
Book
)
5 editions published between 1995 and 1996 in English and held by 226 WorldCat member libraries worldwide
5 editions published between 1995 and 1996 in English and held by 226 WorldCat member libraries worldwide
From topology to computation : proceedings of the Smalefest
by
Morris W Hirsch(
Book
)
12 editions published between 1990 and 1993 in English and held by 194 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
12 editions published between 1990 and 1993 in English and held by 194 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
)
11 editions published in 1997 in English and German and held by 156 WorldCat member libraries worldwide
This book contains a collection of 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 Rio 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 proceedings of the first FoCM conference will give the reader an idea of the state of the art in this emerging discipline
11 editions published in 1997 in English and German and held by 156 WorldCat member libraries worldwide
This book contains a collection of 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 Rio 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 proceedings of the first FoCM conference will give the reader an idea of the state of the art in this emerging discipline
Stabilité globale des systèmes dynamiques
by
Michael Shub(
Book
)
17 editions published between 1978 and 1980 in 3 languages and held by 149 WorldCat member libraries worldwide
17 editions published between 1978 and 1980 in 3 languages and held by 149 WorldCat member libraries worldwide
Complexity and real computation
by
Lenore Blum(
)
4 editions published between 1984 and 1998 in English and held by 22 WorldCat member libraries 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 22 WorldCat member libraries 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
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."
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
)
3 editions published in 1998 in English and held by 6 WorldCat member libraries worldwide
3 editions published in 1998 in English and held by 6 WorldCat member libraries worldwide
Stable ergodicity and stable accessibility
by
Charles 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."
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."
The identity is best for 2 x 2 real matrices
by Debra 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 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
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
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
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
On a theory of computation and complexity over the real numbers : NP completeness, recursive functions and universal machines
by
Lenore Blum(
Book
)
1 edition published in 1988 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 3 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
How many eigenvalues of a random matrix are real?
by A 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
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Related Identities
 Hirsch, Morris W. 1933 Author Editor
 Pugh, C. C. (Charles Chapman) 1940
 Smale, Stephen 1930 Author
 Fathi, Albert Other Editor
 Langevin, Remi Other Editor
 Renegar, James 1955 Editor
 Marsden, Jerrold E. Editor
 Cucker, Felipe 1958 Author Editor
 Blum, Lenore Author
 Smale, Steve
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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 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