Spectral invariants of periodic nonautonomous discrete dynamical systems

Alves, João Ferreira; Málek, Michal; Silva,  Luís

http://hdl.handle.net/10400.21/6004

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
Spectral invariants of periodic nonautonomous discrete dynamical systems.pdf		370.5 KB	Adobe PDF	Download

Send Feedback

Authors

Alves, João Ferreira

Málek, Michal

Silva, Luís

Abstract(s)

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

Keywords

Nonautonomous discrete dynamical systems Interval maps Zeta functions Spectral invariants Topological entropy

URI

http://hdl.handle.net/10400.21/6004

Citation

ALVES, João Ferreira; MÁLEK, Michal; SILVA, Luís - Spectral invariants of periodic nonautonomous discrete dynamical systems. Journal of Mathematical Analysis and Applications. ISSN. 0022-247X. Vol. 430, N.º 1 (2015), pp. 85-97.