Use this URL to cite or link to this record in EThOS:
Title: Invariant manifolds of homoclinic orbits : super-homoclinics and multi-pulse homoclinic loops
Author: Bakrani Balani, Sajjad
ISNI:       0000 0004 9357 1901
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2020
Availability of Full Text:
Access from EThOS:
Access from Institution:
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.
Supervisor: Turaev, Dimitry ; Lamb, Jeroen Sponsor: European Union ; European Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral