Advanced Topics in the Theory of Dynamical Systems

Advanced Topics in the Theory of Dynamical Systems covers the proceedings of the international conference by the same title, held at Villa Madruzzo, Trento, Italy on June 1-6, 1987. The conference reviews research advances in the field of dynamical systems.

This book is composed of 20 chapters that explore the theoretical aspects and problems arising from applications of these systems. Considerable chapters are devoted to finite dimensional systems, with special emphasis on the analysis of existence of periodic solutions to Hamiltonian systems. Other chapters deal with infinite dimensional systems and the developments of methods in the general approach to existence and qualitative analysis problems in the general theory, as well as in the study of particular systems concerning natural sciences. The final chapters discuss the properties of hyperbolic sets, equivalent period doubling, Cauchy problems, and quasiperiodic solitons for nonlinear Klein-Gordon equations.

This book is of value to mathematicians, physicists, researchers, and advance students.

List of Contributors

Preface

The Solutions of the Nonlinear Klein-Gordon Equation Near a Steady State

Generalized Melnikov Functions and Existence of Bounded Solutions in Systems with Parameters

On the Well-Posedness of the Euler flow in Bounded Domains

A New Proof of the Existence of a Brake Orbit

Second-Order Retarded Functional Differential Equations: Generic Properties

An Ergodic Decomposition of Invariant Measures for Discrete Semiflows on Standard Borel Spaces

Center Unstable Manifolds in Quasiperiodic and Averaging Systems

Periodic Solutions of Hamiltonian Systems Near Equilibrium: Resonances and their Detuning

On Semigroups and Population

Compact Attractors and Singular Perturbations

On the Spectrum of Invariant Sets for Dissipative Semiflows and the Existence of Inertial Manifolds

A Characterization of Centres Via First Integrals

On L2 Stability of Stationary Navier-Stokes Flow in Exterior Domains

On the Ck-Integrability of some Toda-Like Hamiltonian Systems

Heteroclinic Connections in Parabolic Equations

Oscillatory Solutions for First Order Delay-Differential Equations

Hyperbolic Sets and Shadowing for Noninvertible Maps

Equivariant Period Doubling

Smooth Manifolds for Multiperiodic Cauchy Problems and Quasiperiodic Solitons for Nonlinear Klein-Gordon Equations on R2

Some Remarks About Persistence for Differential Systems and Processes