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.

  Full text to download in external service

Year 2013

• Partial hyperbolicity and central shadowing

  Publication

  • S. Kryzhevich
  • S. Tikhomirov

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS - Year 2013

  We study shadowing property for a partially hyperbolic diffeomor- phism f. It is proved that if f is dynamically coherent then any pseudotrajec- tory can be shadowed by a pseudotrajectory with “jumps” along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.

  Full text available to download

Year 2011

• Firing map of an almost periodic input function

  Publication

  • W. Marzantowicz
  • J. Signerska-Rynkowska

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS - Year 2011

  In mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...

  Full text available to download

• Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds

  Publication

  • G. Graff
  • J. Jezierski

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS - Year 2011

  Let M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.

  Full text available to download

Year 2006

• Fixed point indices of iterations of C^1 maps in R^3

  Publication

  • G. Graff
  • P. Nowak-Przygodzki

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS - Year 2006

  W przypadku gładkiego odwzorowania w R^3 dowiedziona została hipoteza Chowa, Malleta-Pareta i Yorka dotycząca postaci ciągów indeksow iteracji oraz podano kompletny opis możliwych ciągów indeksow.

  Full text to download in external service