Rok 2019

• Detecting coupling directions with transcript mutual information: A comparative study

  Publikacja

  • J. Amigó
  • B. Graff
  • G. Graff
  • R. Monetti
  • K. Tessmer

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B - Rok 2019

  Causal relationships are important to understand the dynamics of coupled processes and, moreover, to influence or control the effects by acting on the causes. Among the different approaches to determine cause-effect relationships and, in particular, coupling directions in interacting random or deterministic processes, we focus in this paper on information-theoretic measures. So, we study in the theoretical part the difference between...

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• Generating sequences of Lefschetz numbers of iterates

  Publikacja

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

  - MONATSHEFTE FUR MATHEMATIK - Rok 2019

  Du, Huang and Li showed in 2003 that the class of Dold–Fermat sequences coincides with the class of Newton sequences, which are defined in terms of socalled generating sequences. The sequences of Lefschetz numbers of iterates form an important subclass of Dold–Fermat (thus also Newton) sequences. In this paper we characterize generating sequences of Lefschetz numbers of iterates.

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• Periodic Points for Sphere Maps Preserving MonopoleFoliations

  Publikacja

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

  - Qualitative Theory of Dynamical Systems - Rok 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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Rok 2018

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

  Publikacja

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

  - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS - Rok 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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