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UID:7425@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20171212T110000
DTEND;TZID=Europe/Paris:20171212T120000
DTSTAMP:20241120T203949Z
URL:https://www.i2m.univ-amu.fr/evenements/dynamical-topology-slovak-space
 s-and-dynamical-compactness/
SUMMARY:Sergiy Kolyada (Institute of Mathematics National Academy of Scienc
 es of Ukraine\, Kiev): Dynamical topology: Slovak spaces and dynamical com
 pactness
DESCRIPTION:Sergiy Kolyada: The area of dynamical systems where one investi
 gates dynamical properties that can be described in topological terms is c
 alled "Topological Dynamics". Investigating the topological properties of 
 spaces and maps that can be described in dynamical terms is in a sense the
  opposite idea. This area is called "Dynamical Topology".\nFor (discrete) 
 dynamical systems given by compact metric spaces and continuous (surjectiv
 e) self-maps\, I will mostly be talking about two new notions: "Slovak Spa
 ce" and "Dynamical Compactness". Slovak Space is a dynamical analogue of t
 he rigid space: a nontrivial compact metric space whose homeomorphism grou
 p is cyclic and generated by a minimal homeomorphism.\nDynamical Compactne
 ss is a new concept of chaotic dynamics. The ω-limit set of a point is a 
 basic notion in theory of dynamical systems and means the collection of st
 ates which "attract" this point while going forward in time. It is always 
 nonempty when the phase space is compact. By changing the time we introduc
 ed the notion of the ω-limit set of a point with respect to a Furstenberg
  family. A dynamical system is called dynamically compact (with respect to
  a Furstenberg family) if for any point of the phase space this ω-limit s
 et is nonempty. A nice property of dynamical compactness:\nall dynamical s
 ystems are dynamically compact with respect to a Furstenberg family if and
  only if this family has the finite intersection property.\nBased on a wor
 k by Tomasz Downarowicz\, Lubomir Snoha and Dariusz Tywoniuk\, and joint w
 orks with Wen Huang\, Danylo Khilko\, Alfred Peris\, Julia Semikina and Gu
 ohua Zhang.\nhttps://www.aimsciences.org/article/doi/10.3934/dcdss.2020074
 \n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Sergiy_Kolyada.jpg
CATEGORIES:Séminaire,Ernest
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