Integer sequences counting periodic points

Simple item page
dc.creatorEverest, Graham
dc.creatorPuri, Yash
dc.creatorWard, Thomas
dc.date2002-04-13
dc.date.accessioned2026-07-07T06:19:51Z
dc.date.available2026-07-07T06:19:51Z
dc.descriptionAn existing dialogue between number theory and dynamical systems is advanced. A combinatorial device gives necessary and sufficient conditions for a sequence of non-negative integers to count the periodic points in a dynamical system. This is applied to study linear recurrence sequences which count periodic points. Instances where the $p$-parts of an integer sequence themselves count periodic points are studied. The Mersenne sequence provides one example, and the denominators of the Bernoulli numbers provide another. The methods give a dynamical interpretation of many classical congruences such as Euler-Fermat for matrices, and suggest the same for the classical Kummer congruences satisfied by the Bernoulli numbers.
dc.identifierhttps://arxiv.org/abs/math/0204173
dc.identifierhttp://arxiv.org/abs/math/0204173
dc.identifierJournal of Integer Sequences, 5:Article 02.2.3, 2002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95170
dc.subjectNumber Theory
dc.subjectDynamical Systems
dc.subject11G07; 37B40
dc.titleInteger sequences counting periodic points
dc.typetext

Files

Collections

arXiv