This book studies nonlocal bifurcations that occur on the boundary of the domain of Morse-Smale systems in the space of all dynamical systems. These bifurcations provide a series of fascinating new scenarios for the transition from simple dynamical systems to complicated ones. The main effects are the generation of hyperbolic periodic orbits, nontrivial hyperbolic invariant sets and the elements of hyperbolic theory. All results are rigorously proved and explained in a uniform way. The foundations of normal forms and hyperbolic theories are presented from the very first stages. The proofs are preceded by heuristic descriptions of the ideas. The book contains new results, and many results have not previously appeared in monograph form.
Rescigno , A. and Richardson , I. ( 1967 ) Struggle for life 1 : two species , Bulletin of Mathematical Biophysics , 29 , 377-88 . Richardson , H.W. ( 1975 - A ) Two disequilibrium models of regional growth , in Cripps , E.L. ( Ed ...
Applications of Bifurcation Theory: Proceedings of an Advanced Seminar
Alan Wilson surveys the range of applications currently devised that have been developed from new advances in mathematics enabling the development of models where sudden changes in equilibrium can be accounted for.
Dynamical systems.
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
... and Brandon Seward, Group Colorings and Bernoulli Subflows, 2015 Michael Aschbacher, Overgroups of Root Groups in Classical Groups, 2015 Mingmin Shen and Charles Vial, The Fourier Transform for Certain HyperKähler Fourfolds, ...
The concept of thickness assigns to every Cantor set in the real line a number from 0 to [infinity symbol].
Progress in Partial Differential Equations: Elliptic and parabolic problems