Erratum: Minimal sets of periods for Morse-Smale diffeomorphisms on orientable compact surfaces. (English) Zbl 1214.37027

Llibre, Jaume; Sirvent, Víctor F.

Houston J. Math. 36, No. 1, 335-336 (2010).

In this erratum to [the authors, Houston J. Math. 35, No. 3, 835–855 (2009; Zbl 1189.37029)] the Lefschetz zeta function of a Morse-Smale diffeomorphism is constructed. The authors prove that in the minimal set of Lefschetz periods there are no even numbers. As a corollary it is proved that if \( g = 2^{n-2} + 1 \), for \( n \geq 2 \) then there is no information in the Lefschetz zeta function to rule out the set of minimal periods is empty.

Reviewer: Angela Slavova (Sofia)

MSC:

37D15	Morse-Smale systems
37E15	Combinatorial dynamics (types of periodic orbits)
37E30	Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37C05	Dynamical systems involving smooth mappings and diffeomorphisms
37C25	Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics

Keywords:

Morse-Smale diffeomorphism; Lefschetz number; zeta function; set of periods; minimal set of periods

Citations:

Zbl 1189.37029