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UID:5026@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20171212T110000
DTEND;TZID=Europe/Paris:20171212T120000
DTSTAMP:20210312T143621Z
URL:https://www.i2m.univ-amu.fr/events/dynamical-topology-slovak-spaces-an
d-dynamical-compactness/
SUMMARY:Dynamical topology: Slovak spaces and dynamical compactness - Sergi
y Kolyada
DESCRIPTION:The area of dynamical systems where one investigates dynamical
properties that can be described in topological terms is called "Topologic
al 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 system
s given by compact metric spaces and continuous (surjective) self-maps\, I
will mostly be talking about two new notions: "Slovak Space" and "Dynamic
al Compactness". Slovak Space is a dynamical analogue of the rigid space:
a nontrivial compact metric space whose homeomorphism group is cyclic and
generated by a minimal homeomorphism.\nDynamical Compactness is a new conc
ept of chaotic dynamics. The ω-limit set of a point is a basic notion in
theory of dynamical systems and means the collection of states which "attr
act" this point while going forward in time. It is always nonempty when th
e phase space is compact. By changing the time we introduced the notion of
the ω-limit set of a point with respect to a Furstenberg family. A dynam
ical system is called dynamically compact (with respect to a Furstenberg f
amily) if for any point of the phase space this ω-limit set is nonempty.
A nice property of dynamical compactness:\nall dynamical systems are dynam
ically compact with respect to a Furstenberg family if and only if this fa
mily has the finite intersection property.\nBased on a work by Tomasz Down
arowicz\, Lubomir Snoha and Dariusz Tywoniuk\, and joint works with Wen Hu
ang\, Danylo Khilko\, Alfred Peris\, Julia Semikina and Guohua Zhang.\nhtt
ps://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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