Canonical Melnikov theory for diffeomorphisms

Autor:	Lomelí, H. E., Meiss, J. D., Ramírez-Ros, R.
Rok vydání:	2007
Předmět:	Nonlinear Sciences - Chaotic Dynamics Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
DOI:	10.1088/0951-7715/21/3/007
Popis:	We study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds. We develop a first-order deformation calculus for invariant manifolds and show that a generalized Melnikov function or Melnikov displacement can be written in a canonical way. This function is defined to be a section of the normal bundle of the saddle connection. We show how our definition reproduces the classical methods of Poincar\'{e} and Melnikov and specializes to methods previously used for exact symplectic and volume-preserving maps. We use the method to detect the transverse intersection of stable and unstable manifolds and relate this intersection to the set of zeros of the Melnikov displacement. Comment: laTeX, 31 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0706.2515 Zobrazit plný text záznamu View this record from Arxiv