Rocky Mountain Journal of Mathematics

Periods of continuous mapson closed surfaces

Juan Luis García Guirao and Jaume Llibre

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The objective of the present work is to present information on the set of periodic points of a continuous self-map on a closed surface which can be obtained using the action of this map on homological groups of the closed surface.

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Rocky Mountain J. Math., Volume 47, Number 4 (2017), 1089-1096.

First available in Project Euclid: 6 August 2017

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Zentralblatt MATH identifier

Primary: 37C05: Smooth mappings and diffeomorphisms 37C25: Fixed points, periodic points, fixed-point index theory 37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems 58F20

Closed surface continuous self-map Lefschetz fixed point theory periodic point set of periods


Guirao, Juan Luis García; Llibre, Jaume. Periods of continuous mapson closed surfaces. Rocky Mountain J. Math. 47 (2017), no. 4, 1089--1096. doi:10.1216/RMJ-2017-47-4-1089.

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  • L. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial dynamics and entropy in dimension one, Adv. Ser. Nonlin. Dynam. 5, World Scientific, Singapore, 2000.
  • R.F. Brown, The Lefschetz fixed point theorem, Scott Foresman and Company, Glenview, IL, 1971.
  • J. Franks, Homology and dynamical systems, CBMS Reg. Conf. Ser. 49, American Mathematical Society, Providence, RI, 1982.
  • J. Franks and J. Llibre, Periods of surface homeomorphisms, Contemp. Math. 117 (1991), 63–77.
  • J.M. Gambaudo and J. Llibre, A note on the set of periods of surface homeomorphisms, J. Math. Anal. Appl. 177 (1993), 627–632.
  • J.L. García Guirao and J. Llibre, Periods of homeomorphisms on surfaces, in Difference equations, L. Alsedà i Soler, et al., eds., Discr. Dynam. Syst. Appl. 180 (2016), 171–178.
  • B. Halpern, Fixed point for iterates, Pacific J. Math. 25 (1968), 255–275.
  • T.Y. Li and J. Yorke, Period three implies chaos, Amer. Math. Month. 82 (1975), 985–992.
  • J.R. Munkres, Elements of algebraic topology, Addison-Wesley, Boston, 1984.
  • A.N. Sharkovskiĭ, Coexistence of cycles of a continuous map of the line into itself, Ukraine Math. Z. 16 (1964), 61–71.
  • J.W. Vicks, Homology theory, An introduction to algebraic topology, Springer-Verlag, New York, 1994.