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DTSTART:20260329T030000
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DTSTAMP:20260425T051709Z
UID:69241e373b547829705210@ist.ac.at
DTSTART:20251216T143000
DTEND:20251216T153000
DESCRIPTION:Speaker: Martin Leguile\nhosted by Kaloshin Group\nAbstract: Wh
 en studying dynamical systems of geometric origin\, a fundamental question
  is whether periodic dataparticularly the length spectrumencodes the under
 lying geometry of the system. In this talk\, I will present several result
 s addressing this question for billiards with hyperbolic behavior. To give
  more structure to the length spectrum\, it is common to augment it with s
 ymbolic data\, resulting in a marked length spectrum (MLS). I will discuss
  the MLS-rigidity for two classes of domains: open dispersing billiards sa
 tisfying the no-eclipse condition\, and Sinai billiards on the two-torus. 
 While the first class exhibits nice symbolic coding\, interesting dynamics
  is confined to a Cantor set\, and then analyticity is required to recover
  the geometry from the MLS. On the contrary\, for Sinai billiards with fin
 ite horizon\, periodic orbits are dense in phase space\, but the lack of s
 tructural stability complicates the marking of the spectrum. I will descri
 be a CAT(0)-based approach to the MLS-rigidity of Sinai billiards\, levera
 ging the approximation of the billiard flow by Anosov geodesic flows. Join
 t work with De Simoi-Kaloshin\, and Finamore.
LOCATION:Oberbank Ballroom\, Central Building\, ISTA
ORGANIZER:esztatec@ist.ac.at
SUMMARY:Martin Leguile: Marked Length Spectral rigidity of dispersing billi
 ards
URL:https://talks-calendar.ista.ac.at/events/6212
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