Dynamical Systems
Proceedings of a Symposium Held at the University of Bahia, Salvador, Brasil, July 26–August 14, 1971
- 1st Edition - January 1, 1973
- Editor: M. M. Peixoto
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 4 6 8 - 6
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 9 1 0 - 8
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… Read more
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Request a sales quoteDynamical 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.
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
- No. of pages: 764
- Language: English
- Edition: 1
- Published: January 1, 1973
- Imprint: Academic Press
- Paperback ISBN: 9781483244686
- eBook ISBN: 9781483269108
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