Dynamical Systems - 1st Edition - ISBN: 9780125503501, 9781483269108

Dynamical Systems

1st Edition

Proceedings of a Symposium Held at the University of Bahia, Salvador, Brasil, July 26–August 14, 1971

Editors: M. M. Peixoto
eBook ISBN: 9781483269108
Imprint: Academic Press
Published Date: 1st January 1973
Page Count: 764
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Description

Dynamical Systems is a collection of papers that deals with the generic theory of dynamical systems, in which structural stability becomes associated with a generic property. Some papers describe structural stability in terms of mappings of one manifold into another, as well as their singularities. One paper examines the theory of polyhedral catastrophes, particularly, the analogues of each of the four basic differentiable catastrophes which map the line. Other papers discuss isolating blocks, the exponential rate conditions for dynamical systems, bifurcation, catastrophe, and a nondensity theorem. One paper reviews the results of functional differential equations which show that a qualitative theory will emerge despite the presence of an infinite dimensionality or of a semigroup property. Another paper discusses a class of quasi-periodic solutions for Hamiltonian systems of differential equations. These equations generalize a well-known result of Kolmogorov and Arnold on perturbations of n-dimensional invariant tori for Hamiltonian systems of n degrees of freedom. The researcher can derive mathematical models based on qualitative mathematical argument by using as "axioms" three dynamic qualities found in heart muscle fibers and nerve axons. The collection can prove useful for mathematicians, students and professors of advanced mathematics, topology or calculus.

Table of Contents


List Of Contributors

Preface

Acknowledgments

Note on Foliations

Polyhedral Catastrophe Theory I : Maps of the Line to the Line

On Rk x Zl-Actions

Morse-Smale R2-Actions on Two-Manifolds

Isolating Blocks, Regularization, and the Three-Body Problem

Exponential Rate Conditions for Dynamical Systems

Bifurcation and Catastrophe

One-Parameter Families of Vector Fields on Two-Manifolds: Another Nondensity Theorem

Some Infinite-Dimensional Dynamical Systems

Stability of Compact Leaves of Foliations

Hyperbolic Closed Geodesies

Generic Vector Bundle Maps

Sur une Généralisation des Structures Feuilletées de Codimension Un

Solution of Generic Linear Equations

Stratifications and Mappings

On Thom-Boardman Singularities

Parabolic Orbits in the Three-Body Problem

Structural Stability on Two-Manifolds

Symmetries and Integrals in Mechanics

On a Nonlinear Problem in Differential Geometry

On a Class of Quasi-Periodic Solutions for Hamiltonian Systems

A Liapounov Unstability Theorem

Hyperbolic Nonwandering Sets on Two-Dimensional Manifolds

Bifurcations of Morse-Smale Dynamical Systems

Factorization of Nonsingular Circle Endomorphisms

Partitions for Circle Endomorphisms

On the Classification of Flows on 2-Manifolds

Indices for Foliations of the Two-Dimensional Torus

Relative Equilibria in Mechanical Systems

Cr Structural Stability Implies Kupka-Smale

Finite Stability Is Not Generic

Some Remarks on Foliations

Singularities of Newtonian Gravitational Systems

Morse-Smale Diffeomorphisms Are Unipotent on Homology

Stability and Genericity for Diffeomorphisms

Bounded Orbits in Mechanical Systems with Two Degrees of Freedom and Symmetry

Stability and Isotopy in Discrete Dynamical Systems

Global Analysis and Economics I: Pareto Optimum and a Generalization of Morse Theory

The Godbillon-Vey Invariant of a Product Foliation Is Zero

Structural Stability and Bifurcation Theory

Generic Bifurcations, of Dynamical Systems

A Nonstabilizable Jet of a Singularity of a Vector Field

Integral Curves Near Mildly Degenerate Singular Points of Vectors Fields

Language et Catastrophes: Eléments pour une Sémantique Topologique

Secondary Obstructions to Integrability

On the Tolerance Stability Conjecture

An Anosov Translation

Foliated S1-Bundles and Diffeomorphisms of S1

Differential Equations for the Heartbeat and Nerve Impulse

Index

Details

No. of pages:
764
Language:
English
Copyright:
© Academic Press 1973
Published:
Imprint:
Academic Press
eBook ISBN:
9781483269108

About the Editor

M. M. Peixoto