On the Lefschetz zeta function for quasi-unipotent maps on the \(n\)-dimensional torus. II: The general case.

DOI10.1016/j.topol.2016.07.020zbMath1372.37082OpenAlexW2496905035MaRDI QIDQ306156

Marcos J. González, Alberto Mendoza, Pedro Berrizbeitia, Victor F. Sirvent

Publication date: 31 August 2016

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2016.07.020

zbMATH Keywords

periodic pointLefschetz numberLefschetz zeta functioncyclotomic polynomialMorse-Smale diffeomorphismquasi-unipotent map

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Combinatorial dynamics (types of periodic orbits) (37E15) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Cyclotomy (11T22) Morse-Smale systems (37D15)

Related Items

On the Lefschetz zeta function for a class of toral maps ⋮ On the Lefschetz zeta function and the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms on products of \(\ell\)-spheres ⋮ On topological entropy, Lefschetz numbers and Lefschetz zeta functions

Cites Work

• Morse-Smale diffeomorphisms on tori
• Periodic points on tori
• The periodic behavior of Morse-Smale diffeomorphisms
• Homology theory and dynamical systems
• Periods and Lefschetz zeta functions
• Minimal sets of periods for torus maps via Nielsen numbers
• On periodic points
• The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups
• Cyclotomic polynomials and minimal sets of Lefschetz periods
• Minimal Lefschetz sets of periods for Morse–Smale diffeomorphisms on then-dimensional torus
• The number of periodic points of smooth maps
• The Dynamics of Morse-Smale Diffeomorphisms on the Torus
• Nielsen Numbers of Maps of Tori
• Some Smooth Maps with Infinitely Many Hyperbolic Peridoic Points
• Period Three Implies Chaos
• Periodic points of holomorphic maps via Lefschetz numbers
• THE BEHAVIOR OF THE INDEX OF PERIODIC POINTS UNDER ITERATIONS OF A MAPPING
• Minimal sets of periods for Morse–Smale diffeomorphisms on non-orientable compact surfaces without boundary
• On the Lefschetz zeta function for quasi-unipotent maps on then-dimensional torus
• Differentiable dynamical systems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item