The Parametrisation method for invariant manifolds of tori in Skew-product lattices and an entire transcendental family with a persistent Siegel disk

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Institution: TDX
Year: 2016
Keywords: Sistemes dinàmics diferenciables; Sistemas dinámicos diferenciales; Differentiable dynamical systems; Invariants; Invariantes; Invariants; Teoria dels reticles; Teoría reticular; Lattice theory; Tor (Geometria); Tor (Geometría); Torus (Geometry); Pertorbació (Matemàtica); Perturbación (Matemáticas); Perturbation (Mathematics); Varietats (Matemàtica); Variedades (Matemáticas); Manifolds (Mathematics); Funcions holomorfes; Funciones holomorfas; Holomorphic functions
Posted: 02/05/2017
Record ID: 2064494
Full text PDF: http://hdl.handle.net/10803/396126


In this thesis we consider two different problems in the theory of dynamical systems. Dynamical systems cover a wide array of subjects, from finite dimensional to infinite dimensional, from analytic to statistical viewpoints and through all gradations in-between. No matter the aspect or tool considered, the study of any dynamical system is concerned in some way or another with the evolution of points through the action of a map. The simplest question to ask of a dynamical system is then which points are invariant? Once we have an answer to this question we can proceed to study the dynamics in a neighborhood of them. In general we find invariant subsets containing the fixed point which provide very relevant information.