Periods of Morse--Smale diffeomorphisms on mathbbSⁿ, mathbbS^m\n \× mathbbSⁿ, \ℂPⁿ and \ℍPⁿ

2020/04/03 by Clara Cufí-Cabré, Jaume Llibre, Cufí-Cabré, Clara +1
Computer Science · Mathematics · Physics and Astronomy · #37C05 #37C25 #58B05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2004.01465

openalex publication_date 2020/04/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study the set of periods of the Morse--Smale diffeomorphisms on the\nn-dimensional sphere mathbbSⁿ, on products of two spheres of arbitrary\ndimension mathbbS^m \× mathbbSⁿ with m \≠ n, on the\nn-dimensional complex projective space \ℂ Pⁿ and\non the n-dimensional quaternion projective space\n\ℍ Pⁿ. We classify the minimal sets of Lefschetz\nperiods for such Morse--Smale diffeomorphisms. This characterization is done\nusing the induced maps on the homology. The main tool used is the Lefschetz\nzeta function.\n

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