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TY  - THES
AU  - Masci, Leonardo
TI  - Abundance of periodic orbits in asymptotically linear Hamiltonian systems
PB  - RWTH Aachen University
VL  - Dissertation
CY  - Aachen
M1  - RWTH-2025-00518
SP  - 1 Online-Ressource : Illustrationen
PY  - 2025
N1  - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University
N1  - Dissertation, RWTH Aachen University, 2025
AB  - In this thesis a twist condition which applies to asymptotically linear Hamiltonian diffeomorphisms of linear phase space is introduced. This twist condition is inspired by the classical Poincaré-Birkhoff theorem on area-preserving maps of the annulus. The main goal of the thesis is to use the twist condition to find periodic points of asymptotically linear Hamiltonian diffeomorphisms. Namely, it is shown that if an asymptotically linear Hamiltonian diffeomorphism, which is non-degenerate and unitary at infinity, satisfies the twist condition, then it must have infinitely many periodic points. To prove this theorem, a construction of Floer homology for asymptotically linear Hamiltonian diffeomorphisms is provided, and a technique to relate the filtered Floer homologies of different iterates of the same asymptotically linear Hamiltonian diffeomorphism is introduced.
LB  - PUB:(DE-HGF)11
DO  - DOI:10.18154/RWTH-2025-00518
UR  - https://publications.rwth-aachen.de/record/1002419
ER  -