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Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms

Abstract

We apply the representation of Lefschetz numbers of iterates in the form of periodic expansion to determine the minimal sets of Lefschetz periods of Morse–Smale diffeomorphisms. Applying this approach we present an algorithmic method of finding the family of minimal sets of Lefschetz periods for Ng, a non-orientable compact surfaces without boundary of genus g. We also partially confirm the conjecture of Llibre and Sirvent (J Diff Equ Appl 19(3):402–417, 2013) proving that there are no algebraic obstacles in realizing any set of odd natural numbers as the minimal set of Lefschetz periods on Ng for any g.

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Category:
Articles
Type:
artykuły w czasopismach
Published in:
Journal of Fixed Point Theory and Applications no. 21,
ISSN: 1661-7738
Language:
English
Publication year:
2019
Bibliographic description:
Graff G., Lebiedź M., Myszkowski A.: Periodic expansion in determining minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms// Journal of Fixed Point Theory and Applications -Vol. 21,iss. 2 (2019), s.-
DOI:
Digital Object Identifier (open in new tab) 10.1007/s11784-019-0680-4
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