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Dynamical Systems in Low Dimensions

Cel

We study dynamical systems on metric spaces (non-compact, in general) given by a continuous action of the (semi-)groups of N, Z and R. The problems considered can be roughly divided into two big topics: minimality and dynamical zeta functions.
Minimality.
Besides proving several basic results in a very general settings we focus on homeomorphisms on (non-compact) surfaces of finite type and three-dimensional flows. In the first case we study existence of minimal systems and sets on given spaces; topological structure of minimal sets; embeddings of Cantor-like and Denjoy-like minimal systems and their properties; construction of dynamically relevant foliation (eg. free foliation) with connection to Brouwer theory; existence of invariant sets for quasi-periodically forced systems on the closed and open annuli. In the latter case we are focused on the Gottschalk conjecture and related problems.
Dynamical zeta functions.
This topic is closely related to topological entropy and topological pressure. We study the notions of the Artin-Mazur, Milnor-Thurston and Ruelle zeta functions for systems on graphs, dendrites and similar continua. We define topological pressure for non-autonomous systems and prove its basic properties. We investigate topological entropy in the non-compact case. One of our main goals here is to contribute to the solution of the Entropy conjecture.

Zaproszenie do składania wniosków

FP7-PEOPLE-ERG-2008
Zobacz inne projekty w ramach tego zaproszenia

Koordynator

UNIVERZITA MATEJA BELA V BANSKEJ BYSTRICI
Wkład UE
€ 45 000,00
Adres
NARODNA 12
974 01 Banska Bystrica
Słowacja

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Region
Slovensko Stredné Slovensko Banskobystrický kraj
Rodzaj działalności
Higher or Secondary Education Establishments
Kontakt administracyjny
Roman Nedela (Prof.)
Linki
Koszt całkowity
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