Author : Naiara V. de Paulo
Release : 2018-03-19
Genre : Mathematics
Kind : eBook
Book Rating : 016/5 ( reviews)

GET EBOOK

Book Synopsis Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in $\mathbb {R}^4$ by : Naiara V. de Paulo

Download or read book Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in $\mathbb {R}^4$ written by Naiara V. de Paulo. This book was released on 2018-03-19. Available in PDF, EPUB and Kindle. Book excerpt: In this article the authors study Hamiltonian flows associated to smooth functions R R restricted to energy levels close to critical levels. They assume the existence of a saddle-center equilibrium point in the zero energy level . The Hamiltonian function near is assumed to satisfy Moser's normal form and is assumed to lie in a strictly convex singular subset of . Then for all small, the energy level contains a subset near , diffeomorphic to the closed -ball, which admits a system of transversal sections , called a foliation. is a singular foliation of and contains two periodic orbits and as binding orbits. is the Lyapunoff orbit lying in the center manifold of , has Conley-Zehnder index and spans two rigid planes in . has Conley-Zehnder index and spans a one parameter family of planes in . A rigid cylinder connecting to completes . All regular leaves are transverse to the Hamiltonian vector field. The existence of a homoclinic orbit to in follows from this foliation.