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Structural stability and morphogenesis : an outline of a general theory of models

Author: René Thom
Publisher: Boca Raton : CRC Press, Taylor & Francis Group, 2018.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: René Thom
ISBN: 9780429493027 0429493029
OCLC Number: 1028553198
Language Note: Translated from French.
Notes: "Advanced Book Program."
"A Chapman & Hall book."
"Published 1989 by Westview Press"--Copyright page.
Description: 1 online resource
Contents: Cover --
Half Title --
Title Page --
Copyright Page --
Publisher's Foreword --
Vita --
Special Preface --
Table of Contents --
CHAPTER 1: INTRODUCTION --
1.1 The Program --
A. The succession of form --
B. Science, and the indeterminism of phenomena --
1.2 The theory of models --
A. Formal models --
B. Continuous models --
1.3 A historicophilosophical digression --
A. Qualitative or quantitative --
B. The shadow of history --
C. An extension of our basic intuition --
1.4 The construction of a model --
A. The catastrophe set --
B. The independence of the substrate --
C. Biological and inert forms --
D. Conclusion --
Appendix: The notion of an object --
CHAPTER 2: FORM AND STRUCTURAL STABILITY --
2.1 The study offorms --
A. The usual sense of fonn or shape --
B. The space of fonns --
C. Structural Stability --
D. Nonfarm fonns --
E. Geometrical fonns --
2.2. Structural stability and scientific observation --
A. The conditions of scientific experiment --
B. The quantum objection --
C. Isomorphic processes --
D. The nature of empirical functions --
E. Regular points of a process --
2.3 Structural stability and models --
CHAPTER 3: STRUCTURAL STABILITY IN MATHEMATICS --
3.1 The general problem --
A. Continuous families and bifurcation --
B. Algebraic geometry --
C. Geometrical analysis --
D. Differential topology --
E. Differential equations --
F. Functional analysis and partial differential equations --
3.2. Algebra and morphogenesis --
A. An example of bifurcation --
B. The universal unfolding of a singularity of finite codimension --
C. An example: the universal unfolding of y = :r' --
D. The general theory of the universal unfolding --
E. The case of a function --
CHAPTER 4: KINEMATIC OF FORMS --
CATASTROPHES --
4.1 Spatial processes --
A. The morphology of a process --
B. Attractors --
C. The partition into basins. 4.2 Mathematical models for regular processes --
A. Static models --
B. Metabolic models --
C. Evolution of fields --
D. Equivalence of models --
E. Isomorphic processes --
4.3 Catastrophes --
A. Ordinary catastrophe points --
B. Essential catastrophe points --
4.4 Morphogenetic fields associated with local catastrophes --
A. Static models --
B. Stable singularities of wave fronts --
C. Metabolic models --
4.5 Preliminary classification of catastrophe --
A. The domain of existence and basin of an attractor --
B. Conflict and bifurcation catastrophes --
4.6 Thermodynamical coupling --
A. Microcanonical entropy --
B. The interaction of two systems --
C. The approach to the equilibrium state with thermodynamical interaction --
D. Polarized dynamics --
E. The pseudogroup of local equivalences of a field --
4.7 The reduced field --
A. The definition of the reduced field --
B. The self-interaction of a field --
the evolution of the reduced field --
CHAPTER 5: ELEMENTARY CATASTROPHES ON R4 ASSOCIATED WITH CONFLICTS OF REGIMES --
5.1 Fields of gradient dynamics and the associated static model --
A. The competition between regimes --
B. Maxwell's convention --
5.2 The algebraic study of point singularities of a potential function --
A. The catastrophe set --
B. Bifurcation strata --
C. A study of isolated singular points --
corank --
D. The residual singularity --
5.3 Catastrophes of corank one --
A. Strata of codimension zero --
B. Strata of codimension one --
1. Strata of fold type --
2. Conflict strata --
C. Strata of codimension two --
1. The transversal intersection of two fold strata --
2. Strata of cusp points and the Riemann-Hugoniot catastrophe --
3. Conflict strata --
4. The transversal intersection of a fold stratum and a conflict stratum --
D. Sttata of codimension three --
1. The swallow's tail --
2. Transition sttata --
3. Conflict sttata. E. Sttata of codimension four: the butterfly --
5.4 Elementary catastrophes of corank two --
A. Umbilics --
B. Classification of umbilics --
C. The morphology of umbilics --
1. The hyperbolic umbilic: the crest of the wave --
2. The elliptic umbilic: the hair --
3. A remark on the terminology --
4. The parabolic umbilic: the mushroom --
D. A general remark on bifurcation catastrophes --
5.5 The morphology of breakers --
5.6 Attractors of a metabolic [leld --
CHAPTER 6: GENERAL MORPHOLOGY --
6.1 The main types of forms and their evolution --
A. Static and metabolic models --
B. Competition of atttactors of a Hamiltonian dynamic --
C. Creation of a new phase --
generalized catastrophes --
1. Lump catastrophes --
2. Bubble catastrophes --
3. Laminar and filament catastrophes --
4. Catastrophes with a spatial parameter --
D. Superposition of catastrophes --
E. Models for a generalized catastrophe --
change of phase --
F. The formalization of a generalized catastrophe --
6.2 The geometry of a coupling --
A. Mean field --
B. Examples of mean fields associated with an elementary catastrophe --
1. The fold --
2. Thecusp --
C. Mean fields associated with a coupling --
D. Mean field, scale, and catastrophes --
6.3 Semantic models --
A. Definition of a chreod --
B. The subchreod of a chreod --
C. The family tree of chreods --
D. Conditional chreods and levels of organization --
E. Examples of semantic models --
1. The diffusion of a drop of ink in water --
2. Feynman graphs in the theory of elementary particles --
F. The analysis of a semantic model --
G. The dynamical analysis of the chreods of a static model --
Appendix: Spiral nebulae --
CHAPTER 7:THE DYNAMIC OF FORMS --
7.1 Models of mechanics --
A. Limitations of classical and quantum models --
B. Determinism --
7.2 Information and topological complexity --
A. The present use of the idea of information. B. The relative nature of complexity --
C. Topological complexity of a form --
D. The choice of a ground form --
E. Complexity in a product space --
7.3 Information, significance, and structural stability --
A. Free interaction --
B. The entropy of a form --
C. Competition of resonances --
D. Information and probability --
7.4 Energy and spatial complexity --
A. The spectrum --
B. Stunn-Liouville theory in several dimensions --
C. Aging of a dynamical system and the evolution of a field toward equilibrium --
7.5 Formal dynamics --
A. The origin of formal dynamics --
B. Phenomena of memory and facilitation --
C. Canalization of equilibrium --
D. Threshold stabilization --
E. Threshold stabilization and the theory of games --
F. Other formal aspects of a coupling: coding --
7.6 Form and information --
Appendix 1: Conservation of energy and the first law of thermodynamics --
Appendix 2: Topological complexity of a dynamic --
Appendix 3: Infinite complexity of geometrical forms --
The space and forms of a fountain space --
The symmetry principle --
CHAPTER 8: BIOLOGY AND TOPOLOGY --
8.1 The topological aspect of biological morphogenesis --
8.2 Form in biology --
the idea of a phenotype --
A. The spatial form --
B. The global form --
8.3 Molecular biology and morphogenesis --
A. The inadequacy of biochemistry --
B. Morphology and biochemistry --
8.4 Information in biology --
Appendix: Vitalism and reductionism --
CHAPTER 9: LOCAL MODELS IN EMBRYOLOGY --
9.1 The variety of local mechanisms of morphogenesis in biology --
9.2 The presentalion of the model --
9.3 A discussion of historical theories --
A. Development of mosaic type --
B. Gradient theories --
9.4 Models in primitive epigenesis of amphibia --
9.5 Models/or the primitive strealc --
A. Gaslnllation in birds --
B. The comparative topology of gaslnllation in vertebrates. 9.6 Models in mean epigenesis --
A. Induction crossed by resonance: glandular scheme --
B. Morphogenesis of a vertebrate limb --
1. The morphogenetic field of a bone --
2. The fonnation of muscles attached to a joint --
9.7 Late epigenesis: some archetypal chreods associated with umbilics --
A. Capture chreods --
B. Genital chreods --
Appendix: Neurulation and the/ormation of the spinal cord --
CHAPTER 10: GLOBAL MODELS FOR A LIVING BEING(METAZOA) --
10.1 The static model --
A. Preamble --
B. The static global model --
C. The geometry of regeneration in planarians --
D. A digression: preformation and epigenesis --
10.2 The metabolic model --
A. Limitations of the static model --
B. The epigenetic polyhedron --
C. The regulation figure --
D. A preliminary description of the global model --
E. Self-reproducing singularities --
F. The mixed model --
10.3 The hydraulic model --
A. Description of the model --
B. Relationship between the hydraulic model and the metabolic model --
C. The dynamic of gametogenesis --
D. Reproduction in the hydraulic model --
E. Interpretation of the animal-vegetal gradient --
F. Interpretation of the internal variables --
10.4 The formal analysis of organogenesis --
A. Origins of organogenesis --
B. Localization of functions --
C. Formalism of reproduction, and the genetic material --
D. Formal effects of localization: the reversibility of transitions and threshold stabilization --
E. Organs of the embryo --
10.5 A theoretical plan of a differentiation catastrophe --
1. The origin of the germ structure --
2. The frequent disappearance of organizing centers in embryology --
3. Polarization --
4. Embryological induction --
5. Abnormal evolutions --
10.6 Examples of organogenesis --
A. Respiration and blood circulation --
1. The origin of the blood circulation --
2. Theblood --
3. The heart --
4. Breathing.
Other Titles: Stabilité structurelle et morphogénèse.
Responsibility: René Thom, Institut des Hautes Etudes Scientifiques ; translated from the French edition, as updated by the author, by D.H. Fowler, University of Warwick.

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