Vela Castro, Javier Gustavo (2026) Symbolic Dynamics and Topological Entropy: A Combinatorial Approach to Dynamical Complexity. Bachelor's Thesis, Mathematics.
|
Text
Thesis-Javier-Vela.pdf Download (752kB) | Preview |
Abstract
The objective of this thesis is to study discrete dynamical systems through the framework of symbolic dynamics. In this approach, the orbits of a system are encoded as sequences of symbols, allowing for its complex behavior to be analyzed in a simpler combinatorial setting. The full shift space and its associated shift map are introduced, and it is demonstrated that this system exhibits chaotic behavior in a topological sense. Furthermore, the connections between interval maps and symbolic systems are examined through the concept of topological conjugacy. Finally, the notion of topological entropy is then analyzed as a quantitative measure of dynamical complexity, and its value is computed for selected examples. These results illustrate how symbolic dynamics provides a useful framework for understanding and classifying chaotic behavior.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Sterk, A.E. and Waalkens, H. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 08 Jul 2026 13:56 |
| Last Modified: | 08 Jul 2026 13:56 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37399 |
Actions (login required)
 |
View Item |