Dynamical Systems  book cover
1st Edition

Dynamical Systems

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ISBN 9780582216211
Published February 22, 1993 by Chapman and Hall/CRC
456 Pages

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Book Description

In at least five countries in Latin America, high level research in the field in taking place. To stimulate this development both at home and abroad, Chilean mathematicians have been promoting international meetings like the III International School of Dynamical Systems, which took place at the Universidad de Santiago de Chile-Santiago in 1990. A number of distinguished mathematicians were present at the meeting, side by side with younger people interested in the subject. Several of the participants submitted original contributions to these proceedings of the school. The topics of the papers are central to dynamics: ergodic theory, real and complex foliations, fractal dimensions, polynomial vector fields, hyperbolicity, and expansive maps. Notes on the ergodic theory of plane billiards are also included. This book will be of particular interest to researchers and graduate students working in mathematics, particularly in ordinary differential equations, bifurcation theory, and dynamical systems. Also those working in mathematical physics and physics.

Table of Contents

Cantor sets, numerical invariants and Perron Frobenius theory
A modulus of stability for the Sil'nikov theorem
Heteroclinic orbits for singularly perturbed differential-difference equations
Simultaneous Hopf bifurcations at the origin and infinity for cubic systems
Nondensity of ()-stable endomorphisms and rough ()-stabilities for endomorphisms
Supplement to homoclinic doubling bifurcation in vector fields
On stable and unstable sets
The fundamental theorem of Sinai-Chernov for dynamical systems with singularities
Singular perturbations of autonomous ordinary differential equations and heteroclinic bifurcation
Expansivity and length expansivity for geodesic flows on surfaces
Rigidity of the C1-centralizer of bidimensional diffeomorphisms
Poisson brackets and dynamics
A note on algebraic solutions of foliations in dimension two
Lines of curvature near hyperbolic principal cycles
Arithmetic, geometry and dynamics in the unit tangent bundle of the modular orbifold
Three dimensional expansive homeomorphisms
Introduction to the ergodic theory of plan billiards

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