Periodic expansion in determining minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms
type: Item
instance of: scholarly article
title: Periodic expansion in determining minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms
zbMATH Open document ID: 1431.37033
author: Grzegorz Graff
author: Małgorzata Lebiedź
author: Adrian Myszkowski
published in: Journal of Fixed Point Theory and Applications
publication date: 2019-06-28T00:00:00Z
review text: The authors present a method for determining the minimal sets of Lefschetz periods of Morse-Smale diffeomorphisms. They apply this method for finding the family of minimal sets for self-maps on a nonorientable compact surface of given genus without boundary. Their algorithm confirms that there are no algebraic obstructions in realizing any set of odd natural numbers as the minimal set of Lefschetz periods on such surfaces.
reviewed by: M. R. Molaei
Mathematics Subject Classification ID: 37D15
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 37E15
Mathematics Subject Classification ID: 37C30
Mathematics Subject Classification ID: 37D40
zbMATH DE Number: 7075055
zbMATH Keywords: Morse-Smale diffeomorphism
zbMATH Keywords: Lefschetz number
zbMATH Keywords: periodic expansion
zbMATH Keywords: zeta function
zbMATH Keywords: set of periods
zbMATH Keywords: nonorientable compact surfaces
MaRDI profile type: Publication
full work available at URL: s11784-019-0680-4
OpenAlex ID: W2921783370
cites work: THE BEHAVIOR OF THE INDEX OF PERIODIC POINTS UNDER ITERATIONS OF A MAPPING
cites work: Mayer-Vietoris property of the fixed point index
cites work: On the Lefschetz zeta function and the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms on products of \(\ell\)-spheres
cites work: Q3342939
cites work: Fixed point indices of iterated maps
cites work: Q3024014
cites work: Q4003421
cites work: Periodic points of holomorphic maps via Lefschetz numbers
cites work: Some Smooth Maps with Infinitely Many Hyperbolic Peridoic Points
cites work: Algebraic periods of self-maps of a rational exterior space of rank 2
cites work: Existence of \(\delta_m\)-periodic points for smooth maps of compact manifold
cites work: Q4952909
cites work: Minimal number of periodic points for smooth self-maps of two-holed 3-dimensional closed ball
cites work: Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
cites work: Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers
cites work: Generating sequences of Lefschetz numbers of iterates
cites work: Dynamical systems on 2- and 3-manifolds
cites work: Periods for Transversal Maps Via Lefschetz Numbers for Periodic Points
cites work: On the set of periods for the Morse–Smale diffeomorphisms on the disc withNholes
cites work: Periodic structure of transversal maps on \(\mathbb C\mathrm P^n\), \(\mathbb H\mathrm P^n\) and \(\mathbb S^p\times\mathbb S^q\)
cites work: Periods of Morse–Smale diffeomorphisms of S2
cites work: Q4924146
cites work: Minimal Lefschetz sets of periods for Morse–Smale diffeomorphisms on then-dimensional torus
cites work: Fixed point indices of planar continuous maps
cites work: Q5713425
cites work: Q4278144
cites work: Periods for transversal maps on compact manifolds with a given homology
cites work: Minimal sets of periods for Morse–Smale diffeomorphisms on non-orientable compact surfaces without boundary
cites work: Q3182308
cites work: Finding periodic points of a map by use of a \(k\)-adic expansion
cites work: An Arithmetic Function Arising From the /phi Function
cites work: Q4772449
cites work: Fermat's Little Theorem and Gauss Congruence: Matrix Versions and Cyclic Permutations
cites work: Q5246224
Wikidata QID: Q128228020
DOI: 10.1007/S11784-019-0680-4
description: scientific article; zbMATH DE number 7075055