Books about Homoclinic from Amazon.com

This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse homoclinic orbits, and a discussion of the subordinate bifurcations that accompany homoclinic bifurcations, including Hénon-like families. The core of the work is the investigation of the interplay between homoclinic tangencies and non-trivial basic sets. The fractal dimensions of these basic sets turn out to play an important role in determining which class of dynamics is prevalent near a bifurcation. The authors provide a new, more geometric proof of Newhouse's theorem on the co-existence of infinitely many periodic attractors, one of the deepest theorems in chaotic dynamics..
Price: $53.00 [Notify me when price goes down.]

Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods Moreover, they apply in a very large number of situations. It was realized many years ago that the solutions of a great number of problems are in effect critical points of functionals. Critical Point Theory and Its Applications presents some of the latest research in the area of critical point theory. Researchers have obtained many new results recently using this approach, and in most cases comparable results have not been obtained with other methods. This book describes the methods and presents the newest applications.

The topics covered in the book include extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. The applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations. Many minimax theorems are established without the use of the (PS) compactness condition.

.
Price: $67.46 [Notify me when price goes down.]

This volume presents new research on normal forms, symmetry, homoclinic cycles, and chaos, from the Workshop on Normal Forms and Homoclinic Chaos held during The Fields Institute Program Year on Dynamical Systems and Bifurcation Theory in November 1992, in Waterloo, Canada. The workshop bridged the local and global analysis of dynamical systems with emphasis on normal forms and the recently discovered homoclinic cycles which may arise in normal forms.

Specific topics covered in this volume include ...

normal forms for dissipative, conservative, and reversible vector fields, and for symplectic maps;

the effects of symmetry on normal forms;

the persistence of homoclinic cycles;

symmetry-breaking, both spontaneous and induced;

mode interactions;

resonances;

intermittency;

numerical computation of orbits in phase space;

applications to flow-induced vibrations and to mechanical and structural systems;

general methods for calculation of normal forms;

chaotic dynamics arising from normal forms.

Of the 32 presentations given at this workshop, 14 of them are represented by papers in this volume..
Price: $108.00 [Notify me when price goes down.]