Decidability of chaos for some families of dynamical systems
| dc.creator | Arbieto, Alexander | |
| dc.creator | Matheus, Carlos | |
| dc.date | 2002-12-06 | |
| dc.date | 2003-02-24 | |
| dc.date.accessioned | 2026-07-07T04:53:36Z | |
| dc.date.available | 2026-07-07T04:53:36Z | |
| dc.description | We show that existence of positive Lyapounov exponents and/or SRB measures are undecidable (in the algorithmic sense) properties within some parametrized families of interesting dynamical systems: quadratic family and Hénon maps. Because the existence of positive exponents (or SRB measures) is, in a natural way, a manifestation of ``chaos'', these results may be understood as saying that the chaotic character of a dynamical system is undecidable. Our investigation is directly motivated by questions asked by Carleson and Smale in this direction. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0212101 | |
| dc.identifier | http://arxiv.org/abs/math/0212101 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65913 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37C99;03D35 | |
| dc.title | Decidability of chaos for some families of dynamical systems | |
| dc.type | text |