Year 2019

• Periodic Points for Sphere Maps Preserving MonopoleFoliations

  Publication

  • G. Graff
  • M. Misiurewicz
  • P. Nowak-Przygodzki

  - Qualitative Theory of Dynamical Systems - Year 2019

  Let S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...

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Year 2018

• Shub’s conjecture for smooth longitudinal maps of S^m

  Publication

  • G. Graff
  • M. Misiurewicz
  • P. Nowak-Przygodzki

  - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS - Year 2018

  Let f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.

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Year 2016

• Periodic points of latitudinal maps of the $m$-dimensional sphere

  Publication

  • G. Graff
  • M. Misiurewicz
  • P. Nowak-Przygodzki

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS - Year 2016

  Let f be a smooth self-map of the m-dimensional sphere Sm. Under the assumption that f preserves latitudinal foliations with the fibres S1, we estimate from below the number of fixed points of the iterates of f. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.

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