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Full-Text Articles in Physical Sciences and Mathematics
Theory Of Invariant Manifold And Foliation And Uniqueness Of Center Manifold Dynamics, Bo Deng
Theory Of Invariant Manifold And Foliation And Uniqueness Of Center Manifold Dynamics, Bo Deng
Department of Mathematics: Faculty Publications
Here we prove that the dynamics on any two center-manifolds of a fixed point of any Ck,1 dynamical system of finite dimension with k ≥ 1 are Ck-conjugate to each other. For pedagogical purpose, we also extend Perron’s method for differential equations to diffeomorphisms to construct the theory of invariant manifolds and invariant foliations at fixed points of dynamical systems of finite dimensions.
Homoclinic Bifurcations With Nonhyperbolic Equilibria, Bo Deng
Homoclinic Bifurcations With Nonhyperbolic Equilibria, Bo Deng
Department of Mathematics: Faculty Publications
A general geometric approach is given for bifurcation problems with homoclinic orbits to nonhyperbolic equilbrium points of ordinary differential equations. It consists of a special normal form called admissible variables, exponential expansion, strong A-lemma, and Lyapnunov- Schmidt reduction for the Poincare maps under Sil'nikov variables. The method is based on the Center Manifold Theory, the contraction mapping principle, and the Implicit Function Theorem.