Silvius, Teun (2026) Persistence of Non-Trivial Equilibria under Approximated Vector Fields. Bachelor's Thesis, Mathematics.
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Abstract
This thesis investigates the persistence of non-trivial equilibria and their stability in one-dimensional dynamical systems under approximation of the vector field. While the trivial equilibrium at x = 0 is preserved in Taylor and Padé approximations of the vector field xf(x), there is no guarantee that the non-trivial equilibria are captured. We analyze the change in equilibrium structure when these schemes are applied to several function classes, namely entire, meromorphic and branch-point functions. By examining properties regarding convergence and disruptions in dynamics, we determine to what extent these approximation techniques achieve topological equivalence between the original and truncated system. The theoretical findings are backed up by numerical experiments.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Jardon Kojakhmetov, H. and Waalkens, H. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 03 Jul 2026 13:43 |
| Last Modified: | 03 Jul 2026 13:43 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37332 |
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