Numerical Methods for Approximation and Visualization of Invariant Manifolds in Dynamical Systems

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Naderi Yeganeh, Hamid | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52396 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Razvan, Mohammad Reza
Abstract:
Invariant manifolds are important objects in the theory of dynamical systems. The stable manifold theorem is a very important theorem about this concept which proves the existence of stable and unstable manifolds in a wide range of dynamical systems. The importance of invariant manifolds encourages us to view their pictures. It helps us to understand their bahavior. For this purpose, at first we need to approximate the invariant manifold we want to visualize. There are several algorithms designed to approximate invariant manifolds. Those algorithms approximate a set of points on an invariant manifold and then provide an approximation of the manifold by the calculated points. Visualizing an invariant manifold can be
very difficult when its dimension is higher than one. In this thesis we discuss about some algorithms and then we show the images of a few invariant manifolds
Keywords:
Dynamical Systems ; Numerical Method ; Invariant Manifolds ; Stable Manifolds ; Unstable Manifolds

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