Dynamical Systems

Treats the dynamics of both iteration of functions and solutions of ordinary differential equations. This book introduces various concepts for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. It concentrates on properties of the whole system or subsets of the system.
This text covers the dynamics of the iteration of functions and solutions of ordinary differential equations. It first introduces many concepts for iteration of functions - where the geometry is simpler - but interprets the results 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 local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects.Features new to this edition include: improved discussion of saddle node bifurcations; a new section on the horseshoe for flows with transverse homoclinic points; material on horseshoes for nontransverse homoclinic points, indicating advances in the understanding of how horseshoes arise; information proving the ergodicity of a hyperbolic toral automorphism; and a new chapter on Hamiltonian systems.