Orbits for products of maps

Pakapongpun, Apisit; Ward, Thomas

Abstract

We study the behaviour of the dynamical zeta function and the orbit Dirichlet series for products of maps. The behaviour under products of the radius of convergence for the zeta function, and the abscissa of convergence for the orbit Dirichlet series, are discussed. The orbit Dirichlet series of the cartesian cube of a map with one orbit of each length is shown to have a natural boundary.

Citation

Pakapongpun, A., & Ward, T. (2014). Orbits for products of maps. Thai Journal of Mathematics, 12(1), 33-44

• Journal Article Type: Article
• Publication Date: 2014-04
• Deposit Date: Feb 28, 2013
• Publicly Available Date: Apr 11, 2013
• Journal: Thai journal of mathematics
• Print ISSN: 1686-0209
• Publisher: Mathematical Association of Thailand
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 1
• Pages: 33-44
• Keywords: Periodic orbits, Natural boundary, Orbit Dirichlet series, Linear recurrence sequence.
• Public URL: https://durham-repository.worktribe.com/output/1466240
• Publisher URL: http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/view/565