TY - BOOK ID - 4863120 TI - Bifurcation without Parameters PY - 2015 SN - 9783319107776 3319107763 9783319107769 3319107771 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Mathematics. KW - Ordinary Differential Equations. KW - Partial Differential Equations. KW - Dynamical Systems and Ergodic Theory. KW - Differentiable dynamical systems. KW - Differential Equations. KW - Differential equations, partial. KW - Mathématiques KW - Dynamique différentiable KW - Mathematics KW - Physical Sciences & Mathematics KW - Calculus KW - Dynamics. KW - Ergodic theory. KW - Differential equations. KW - Partial differential equations. KW - Partial differential equations KW - 517.91 Differential equations KW - Differential equations KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Physics KW - Statics KW - Math KW - Science KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Global analysis (Mathematics) KW - Topological dynamics UR - https://www.unicat.be/uniCat?func=search&query=sysid:4863120 AB - Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points. ER -