Dynamical Systems: Stability, Symbolic Dynamics, and Chaos 2nd edition [Kõva köide]

New edition of a graduate textbook whose main topic is the dynamics induced by iteration of a function or by the solutions of ordinary differential equations. This edition features a revised discussion of the saddle node bifurcation, a new section on the horseshoe for a flow with a transverse homoclinic point, information proving the ergodicity of a hyperbolic toral automorphism, and a new chapter on Hamiltonian systems. The focus is on multidimensional systems of real variables. Annotation c. by Book News, Inc., Portland, Or.

Several distinctive aspects make Dynamical Systems unique, including:

treating the subject from a mathematical perspective with the proofs of most of the results included

providing a careful review of background materials

introducing ideas through examples and at a level accessible to a beginning graduate student

focusing on multidimensional systems of real variables

The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects.

The second edition of this popular text continues to treat dynamical systems from a mathematical perspective centering on multidimensional systems of real variables. At a level accessible to beginning graduate students, it addresses the dynamics of both the iteration of functions and solutions of ordinary differential equations. This edition includes material on horsehoes, an additional chapter on Hamiltonian systems, a revised discussion of the saddle node bifurcation, and proof of the ergodicity of a hyperbolic toral automorphism. Numerous exercises help readers understand the theorems presented and master the techniques of the proofs and topics under consideration.