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Orbit-counting in non-hyperbolic dynamical systems | | G. Everest
; R. Miles
; S. Stevens
; T. Ward
; PostScript
; PDF
; Other formats
; | | Date: |
22 Nov 2005 | | Subject: | Dynamical Systems; Number Theory | | 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. | | Source: | arXiv, math/0511569 | | Services: | Forum | Review | PDF | Favorites | |
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