G. Everest
Orbit-counting in non-hyperbolic dynamical systems
Everest, G.; Miles, R.; Stevens, S.; Ward, T.
Authors
R. Miles
S. Stevens
T. Ward
Abstract
There are well-known analogs of the prime number theorem and Mertens' theorem for dynamical systems with hyperbolic behaviour. Here we consider the same question for the simplest non-hyperbolic algebraic systems. The asymptotic behaviour of the orbit-counting function is governed by a rotation on an associated compact group, and in simple examples we exhibit uncountably many different asymptotic growth rates for the orbit-counting function. Mertens' Theorem also holds in this setting, with an explicit rational leading coefficient obtained from arithmetic properties of the non-hyperbolic eigendirections.
Citation
Everest, G., Miles, R., Stevens, S., & Ward, T. (2007). Orbit-counting in non-hyperbolic dynamical systems. Journal für die reine und angewandte Mathematik, 2007(608), 155-182. https://doi.org/10.1515/crelle.2007.056
Journal Article Type | Article |
---|---|
Publication Date | Jan 1, 2007 |
Deposit Date | Oct 12, 2012 |
Publicly Available Date | Dec 14, 2012 |
Journal | Journal für die reine und angewandte Mathematik |
Print ISSN | 0075-4102 |
Electronic ISSN | 1435-5345 |
Publisher | De Gruyter |
Peer Reviewed | Peer Reviewed |
Volume | 2007 |
Issue | 608 |
Pages | 155-182 |
DOI | https://doi.org/10.1515/crelle.2007.056 |
Public URL | https://durham-repository.worktribe.com/output/1502557 |
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