### Abstract

In this paper, by using the Lefschetz zeta function, we characterize the set of periods of the Morse-Smale diffeomorphisms defined on the two-dimensional torus for every homotopy class. Our characterization distinguish between the class of orientation-preserving and orientation-reversing Morse-Smale diffeomorphisms. Moreover, we also characterize the minimal set of periods of the Morse-Smale diffeomorphisms. Copyright © 2012 Watam Press.

Original language | English |
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Pages (from-to) | 471-484 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis |

Volume | 19 |

Issue number | 4 |

Publication status | Published - 24 Aug 2012 |

### Keywords

- Lefschetz number
- Morse-Smale diffeomorphism
- Set of periods
- Zeta function

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## Cite this

Guirao, J. L. G., & Llibre, J. (2012). The set of periods for the morse-smale diffeomorphisms on T

^{2}.*Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis*,*19*(4), 471-484.