Periodic orbits of a dynamical system related to a knot

2009/06/16 by Lilya Lyubich, Lyubich, Lilya
Computer Science · Mathematics · #54H20 #57Q45 #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.DS #math.GT #msc:54H20 #msc:57Q45 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0906.2790

13 pages

arxiv created 2009/06/16 · openalex publication_date 2009/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the space of all representations of the commutator subgroup of a knot group into Z/p, p is prime. As proven by D. Silver and S. Williams, this space can be completely described by a finite oriented graph. We describe the lengths of cycles in this graph.

Related

• On cycles and coverings associated to a knot
• Hamiltonicity of Transitive Graphs Whose Automorphism Group Has \Z_p as Commutator Subgroups
• Primes, knots and periodic orbits
• Commuting graph of A-orbits
• Skein Algebras of the solid torus and symmetric spatial graphs