Zakład Układów Dynamicznych
Kierownik:
- prof. dr hab. Feliks Przytycki (profesor)
email
pok. 417, tel.: 022 5228 161
Pracownicy:
- dr hab. Krzysztof Frączek (adiunkt)
(X.2006 - IX.2009)
email - dr Grzegorz Graff (adiunkt) (X.2008 - IX.2009)
- dr Eugene Gutkin (adiunkt)
(VII.2007 - VII.2009)
email - mgr Joanna Jaszuńska (asystent)
(IX.2006 - XII.2008)
email
223, tel.: 022 5228 223 - prof. dr hab. Mariusz Lemańczyk (profesor)
(IV.2006 - IX.2009)
email - dr Tomas Persson (adiunkt) (I.2009 - XII.2010)
- dr hab. Michał Rams (adiunkt)
email
pok. 417, tel.: 022 5228 161 - dr Michał Stukow (adiunkt)
(X.2007 - IX.2008)
email - dr hab. Tomasz Szarek (docent)
(II.2008 - VII.2008)
email - prof. dr hab. Paweł Walczak (profesor)
email
O Zakładzie
The Laboratory exists since 2006. Before it was a part of the Laboratory of Functional Analysis. Its research staff includes: Feliks Przytycki (the head, permanent position), Michal Rams (long term), Pawel Walczak (part time), Krzysztof Frączek (part time), Carlos Cabrera (2006/2007), Neil Dobbs (2007/2008). The main fields of research run in the Laboratory are holomorphic dynamics in dimension 1, dynamical fractals and geometric dimensions, foliations and other topics in dynamical systems. It runs dynamical systems seminar and cooperates with Dynamical Systems Laboratory at Warsaw University. It is involved in the European FP6 Marie Curie programs ToK Deterministic and Stochastic Dynamics, Fractals, Turbulence (SPADE2) and RTN Conformal Structures and Dynamics (CODY).
1. Iteration of holomorphic maps
- F. Przytycki, Conical limit sets and Poincaré exponent for iterations of rational functions, Transactions of the AMS, 351.5 (1999), 2081-2099.
- F. Przytycki, J. Rivera-Letelier, S. Smirnov, Equivalence and topological invariance of conditions for non-uniform hyperbolicity in iteration of rational maps, Inventiones Mathematicae 151 (2003), 29-63.
- F. Przytycki, J. Rivera-Letelier, Statistical properties of Topological Collet-Eckmann maps. Annales Scientifiques de l'École Normale Superieure. 4e série, t.40, (2007), 135-178.
- N. Dobbs, B. Skorulski, Non-existence of absolutely continuous invariant probabilities for exponential maps, Fund. Math. 198 (2008), 283-287
2. Dynamics, complexity, ergodic theory
- K. Frączek, L. Polterovich, Growth and mixing, to appear in Journal of Modern Dynamics.
- E. Gutkin, M. Rams, Growth rates for geometric complexities and counting functions in polygonal billiards, to appear.
- F. Przytycki, W. Marzantowicz, Entropy Conjecture for continuous maps of nilmanifolds, to appear in Israel Journal of Mathematics.
3. Fractals, iterated function systems, thermodynamical formalism and geometric measure theory point of view
- M. Rams, Y.Peres, K.Simon, B.Solomyak, Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets, Proc. of Amer. Math. Soc., 129 (2001), 2689-2699.
- M. Rams, Packing dimension estimation for exceptional parameters Israel J. of Math., 130 (2002), 125-144.
- M. Rams, Measures of maximal dimension for linear horseshoes, Real Anal. Exchange, 31 (2005/06), 55-62.
4. Structures on manifolds, group actions, foliations
- B. Hajduk, R. Walczak, Symplectic forms invariant under free circle actions on 4-manifolds, Trans. AMS 358 (2006), 1953-1970
- P. Walczak, Dynamics of Foliations, Groups and Pseudogroups, Monografie Matematyczne Vol.64 New Series, Birkhäuser, 2004.
