Investigation of nonhyperbolic dynamical systems
Published in Technische Universität Dresden, 2019
Abstract
The aim of this thesis is to analyze the effect of nonhyperbolicity on a nonlinear dynamical system. The focus lies on the distribution of periodic points on the attractor. Since unstable periodic orbits are the basis for many calculations in dynamical systems theory, their distribution is of special importance. Two systems are regarded in this thesis: the nonhyperbolic Hénon map and the hyperbolic dissipative baker map. For both systems, the unstable periodic orbits and other important quantities are calculated. Starting from a qualitative approach, the presence and location of parts of the Hénon attractor without periodic points and their dependence on the period length is discussed. Later, quantitative tools for analyzing the distribution of periodic points on the attractor are developed and applied to the Hénon map. Finally, an explanation for the observed gaps on the Hénon attractor is sketched, connecting them to generating partitions and symbolic dynamics.
Recommended citation: Schaumann, F. (2019). Investigation of nonhyperbolic dynamical systems. Bachelor thesis, Technische Universität Dresden. PuRe: hdl.handle.net/21.11116/0000-0006-CFAD-F
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