A complex ruelle-perron-frobenius theorem for infinite markov shifts with applications to renewal theory

Marc Kesseböhmer; Sabrina Kombrink

doi:10.3934/dcdss.2017016

A complex ruelle-perron-frobenius theorem for infinite markov shifts with applications to renewal theory

Marc Kesseböhmer^*, Sabrina Kombrink

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Mathematik

Universität Bremen

10 Zitate (Scopus)

Abstract

We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet setting. As an application we obtain an extension of renewal theory in symbolic dynamics, as developed by S. P. Lalley and in the sequel generalised by the second author, now covering the infinite alphabet case.

Originalsprache	Englisch
Zeitschrift	Discrete and Continuous Dynamical Systems - Series S
Jahrgang	10
Ausgabenummer	2
Seiten (von - bis)	335-352
Seitenumfang	18
ISSN	1937-1632
DOIs	https://doi.org/10.3934/dcdss.2017016
Publikationsstatus	Veröffentlicht - 01.04.2017

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10.3934/dcdss.2017016

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N2 - We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet setting. As an application we obtain an extension of renewal theory in symbolic dynamics, as developed by S. P. Lalley and in the sequel generalised by the second author, now covering the infinite alphabet case.

AB - We prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet setting. As an application we obtain an extension of renewal theory in symbolic dynamics, as developed by S. P. Lalley and in the sequel generalised by the second author, now covering the infinite alphabet case.

UR - https://www.scopus.com/pages/publications/85010041713

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DO - 10.3934/dcdss.2017016

M3 - Journal articles

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A complex ruelle-perron-frobenius theorem for infinite markov shifts with applications to renewal theory

Abstract

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