Invariant manifolds of homoclinic orbits: super-homoclinics and multi-pulse homoclinic loops
File(s)
Author(s)
Bakrani Balani, Sajjad
Type
Thesis
Abstract
Consider a Hamiltonian flow on R4 with a hyperbolic equilibrium O and a transverse homoclinic orbit Γ. In this thesis, we study the dynamics near Γ in its energy level when it leaves and enters O along strong unstable and strong stable directions, respectively. In particular, we provide necessary and sufficient conditions for the existence of the local stable and unstable invariant manifolds of Γ. We then consider the case in which both of these manifolds exist. We globalize them and assume they intersect transversely. We prove that near any orbit of this intersection, called super-homoclinic, there exist infinitely many multi-pulse homoclinic loops.
Version
Open Access
Date Issued
2020-02
Date Awarded
2020-07
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
Advisor
Turaev, Dimitry
Lamb, Jeroen
Sponsor
European Unions
European Research Council
Grant Number
Grant Agreement Number 643073
No 339523
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)