Periodic orbits of linear endomorphisms on the 2-torus and its lattices

Details Periodic orbits of linear endomorphisms on the 2-torus and its lattices Periodic orbits of linear endomorphisms on the 2-torus and its lattices

2008-08-26

arxiv.org/abs/0808.3489v1

Nonlinearity 21 (2008) 2427-2446

Mathematics

Dynamical Systems

22 pages

Scientific paper

10.1088/0951-7715/21/10/012

Counting periodic orbits of endomorphisms on the 2-torus is considered, with special focus on the relation between global and local aspects and between the dynamical zeta function on the torus and its analogue on finite lattices. The situation on the lattices, up to local conjugacy, is completely determined by the determinant, the trace and a third invariant of the matrix defining the toral endomorphism.

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