Multiple periodic solutions of asymptotically linear Hamiltonian systems via Conley index theory
نویسندگان
چکیده
منابع مشابه
MULTIPLE PERIODIC SOLUTIONS FOR A CLASS OF NON-AUTONOMOUS AND CONVEX HAMILTONIAN SYSTEMS
In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.
متن کاملPoincaré-birkhoff Fixed Point Theorem and Periodic Solutions of Asymptotically Linear Planar Hamiltonian Systems
This work, which has a self contained expository character, is devoted to the Poincaré-Birkhoff (PB) theorem and to its applications to the search of periodic solutions of nonautonomous periodic planar Hamiltonian systems. After some historical remarks, we recall the classical proof of the PB theorem as exposed by Brown and Neumann. Then, a variant of the PB theorem is considered, which enables...
متن کاملAn Index Theorem for Non Periodic Solutions of Hamiltonian Systems
We consider a Hamiltonian setup (M, ω,H,L,Γ,P), where (M, ω) is a symplectic manifold, L is a distribution of Lagrangian subspaces in M, P a Lagrangian submanifold of M, H is a smooth time dependent Hamiltonian function on M and Γ : [a, b] 7→ M is an integral curve of the Hamiltonian flow ~ H starting at P . We do not require any convexity property of the Hamiltonian function H . Under the assu...
متن کاملConnecting Fast-slow Systems and Conley Index Theory via Transversality
Geometric Singular Perturbation Theory (GSPT) and Conley Index Theory are two powerful techniques to analyze dynamical systems. Conley already realized that using his index is easier for singular perturbation problems. In this paper, we will revisit Conley’s results and prove that the GSPT technique of Fenichel Normal Form can be used to simplify the application of Conley index techniques even ...
متن کاملMorse Theory for Periodic Solutions of Hamiltonian Systems and the Maslov Index
In this paper we prove Morse type inequalities for the contractible 1-periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the symplectic form and the first Chern class of the tangent bundle vanish over q ( M ) . The proof is based on a version of infinite dimensional Morse theory which is due to Floer. The key point is an ind...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topological Methods in Nonlinear Analysis
سال: 2004
ISSN: 1230-3429
DOI: 10.12775/tmna.2004.005