Harten, M.J. van (2021) Chaos in Newton's method. Master's Thesis / Essay, Mathematics.
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Abstract
This thesis focusses on the map T (x) = 1/2 * (x − 1/x ). It originates from Newton’s method of finding the zeros of z^2 + 1 on the real line. The dynamics of the dynamical system are investigated. Different definitions of chaos are considered and we prove that T is chaotic according to some of these definitions. Furthermore, using ergodic theory, we find the probability density function for the invariant measure. Using Birkhoff’s ergodic theorem we determine the Lyapunov exponent.
| 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: | 09 Jul 2021 11:25 |
| Last Modified: | 09 Jul 2021 11:25 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/25034 |
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