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Finite type coarse expanding conformal dynamics
| Content Provider | Semantic Scholar |
|---|---|
| Author | Häissinsky, Peter |
| Copyright Year | 2008 |
| Abstract | We continue the study of noninvertible topological dynamical systems with expanding behavior. We introduce the class of finite type systems which are characterized by the condition that, up to rescaling and uniformly bounded distortion, there are only finitely many iterates. We show that subhyperbolic rational maps and finite subdivision rules (in the sense of Cannon, Floyd, Kenyon, and Parry) with bounded valence and mesh going to zero are of finite type. In addition, we show that the limit dynamical system associated to a selfsimilar, contracting, recurrent, level-transitive group action (in the sense of V. Nekrashevych) is of finite type. The proof makes essential use of an analog of the finiteness of cone types property enjoyed by hyperbolic groups. Mathematics Subject Classification (2010). 37F20, 37B50, 20F67, 20E08, 37E99. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://hal.archives-ouvertes.fr/hal-00250031/document |
| Alternate Webpage(s) | http://hal.archives-ouvertes.fr/docs/00/25/00/31/PDF/finitetype.pdf |
| Alternate Webpage(s) | http://www.ems-ph.org/journals/show_pdf.php?iss=3&issn=1661-7207&rank=2&vol=5 |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Analog Arabic numeral 0 Complex dynamics Contract agreement Distortion Dynamical system Finite subdivision rule Happiness Map PARRY Rule (guideline) Self-similarity Subdivision surface Type system |
| Content Type | Text |
| Resource Type | Article |
