DS-LOWDIM
Dynamical Systems in Low Dimensions
| Coordinatore | Univerzita Mateja Bela v Banskej Bystrici
Organization address
postcode: 97401 contact info |
| Nazionalità Coordinatore | Slovakia [SK] |
| Totale costo | 45˙000 € |
| EC contributo | 45˙000 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-ERG-2008 |
| Funding Scheme | MC-ERG |
| Anno di inizio | 2009 |
| Periodo (anno-mese-giorno) | 2009-04-15 - 2012-04-14 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 | Univerzita Mateja Bela v Banskej Bystrici | SK | coordinator | 45˙000.00 |
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Obiettivo del progetto (Objective)
'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.'