Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R
- ISBN-10
- 1470428016
- ISBN-13
- 9781470428013
- Category
- Hamiltonian systems
- Pages
- 105
- Language
- English
- Published
- 2018-03-19
- Publisher
- American Mathematical Soc.
- Authors
- Naiara V. de Paulo, Pedro A. S. Salomão
Description
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.
Get the book
Similar books
-
Nonlinear Waves and Weak Turbulence
By Vladimir Evgenʹevich ZakharovADVANCES IN THE MATHEMATICAL SCIENCES EDITORIAL COMMITTEE V. I. ARNOLD S. G. GINDIKIN V. P. MASLOV Translation edited by A. B. Sossinsky 1991 Mathematics Subject Classification . Primary 76B15 , 76C20 ; Secondary 35Q35 , 35Q53 .
-
Many-particle Hamiltonians: Spectra and Scattering
By Robert Adolʹfovich MinlosThis collection deals with several different topics related to the construction and spectral analysis of Hamiltonians of various systems arising in mathematical physics.
-
Integrable Hamiltonian Systems on Complex Lie Groups
By Velimir JurdjevicIn all these cases I4 can be described by a single parameter e as I = 2* = a(w – ea) that is an integral of motion for the Hamiltonian 1 1 H = #(M: + M%) + * M: + b1p1 + b2p2 ([Ju3] and (KoK])). 5. The remaining case, not usually ...
-
New Results in the Theory of Topological Classification of Integrable Systems
By A. T. FomenkoLiouville tori ( with singularities ) and in the nonresonant case this foliation depends only on the system v ( that is ... The first step in the study of the phase topology of the integrable system v consists of the study of the ...
-
Integrable Systems and Random Matrices: In Honor of Percy Deift : Conference on Integrable Systems, Random Matrices, and Applications in...
By Carlos Tomei, Luen-Chau Li, Jinho Baik... semiclassical asymptotics for the sine-Gordon equation (5.2) from a fully discrete Riemann–Hilbert problem. In both ... nonlinear waves. References [1] J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin, and P. D. Miller, Discrete orthogonal ...
-
Hamiltonian Systems and Their Integrability
By Mich'le Audin"This book presents some modern techniques in the theory of integrable systems viewed as variations on the theme of action-angle coordinates.