Chaotic dynamics in a periodically forced fold-and-twist map

IJpma, Ruben (2022) Chaotic dynamics in a periodically forced fold-and-twist map. Master's Thesis / Essay, Mathematics.

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Abstract

Non-invertible planar maps with folds have proven to be a generous source of folded chaotic attractors, although rigorous proofs for their Hénon-like structure are still sought after. The folding maps provide interesting obstacles when embarking upon constructing such proofs, but they also provide a new source for so-called quasi-periodic Hénon-like attractors. Such attractors coincide with the closure of the unstable manifold of a quasi-periodic invariant circle, on which the dynamics are loosely speaking ‘Hénon-like product quasi-periodic’. We provide numerical evidence for such attractors in a periodically driven fold-and-twist map, occurring for sets of parameters with positive measure. We also find that discovering promising proof strategies for the existence of these attractors remains troublesome, due to the non-dissipativity of the fold-and-twist map, and unwieldy changes in periodicity of saddle points when perturbing parameters.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Sterk, A.E. and Jardon Kojakhmetov, H.
Degree programme:	Mathematics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	22 Sep 2022 16:07
Last Modified:	22 Sep 2022 16:07
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/28755

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