Extreme Value Laws for the Generalised Doubling Map Process

Boer, Björn-Sebastiaan (2020) Extreme Value Laws for the Generalised Doubling Map Process. Master's Thesis / Essay, Mathematics.

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Abstract

While it is usually not possible to fully describe the behaviour of a chaotic dynamical system, in certain cases it is possible to derive its asymptotic behaviour. Extreme value theory is the study of looking at extreme values of such a chaotic dynamical system, and prove the asymptotic behaviour of these extreme values. In this paper, we will derive the asymptotic behaviour of the (generalised) doubling map using two methods. First by exactly solving a recursion formula and then using Tannery’s theorem, and alternatively by applying properties of generalised Fibonacci sequences to values that satisfy the recursive relation. Finally, we will interpret the obtained results using extreme value theory.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Sterk, A.E. and Waalkens, H.
Degree programme:	Mathematics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	02 Jun 2020 10:36
Last Modified:	02 Jun 2020 10:36
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/21983

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