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.
|Journal||Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis|
|Publication status||Published - 24 Aug 2012|
- Lefschetz number
- Morse-Smale diffeomorphism
- Set of periods
- Zeta function