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SUMMARY:Dynamical Systems Seminars 
DTSTART;VALUE=DATE-TIME:20260806T143000Z
DTEND;VALUE=DATE-TIME:20260806T163000Z
DTSTAMP;VALUE=DATE-TIME:20260807T032206Z
UID:indico-event-11488@ictp.it
DESCRIPTION:\n16:30-17:15 Rubio Gunawan (SISSA)\nSmooth Circle Covering wi
 th a Physical Measure on a Hyperbolic Repelling Fixed Point\n\n\n\nAbstrac
 t:\nWe construct an example of a smooth (C-infinity) circle covering map t
 opologically conjugate to the doubling map\, such that it has a physical m
 easure supported on a hyperbolic repelling fixed point. By relaxing the sm
 ooth condition at a single point\, we also construct an example where the 
 basin of the physical measure has full measure. A key technical step is a 
 realization method of independent interest\, which gives a canonical way t
 o construct a full branch map given its induced map.\n\n17:30-18:15 Sergio
  Romana (Sun Yat-sen University\, China)\nBirkhoff Spectra for Hyperbolic 
 Dynamics: Density\, Rigidity\, and Geometric Applications\n\nAbstract:\nTh
 is lecture presents a systematic study of Birkhoff spectra for hyperbolic 
 dynamical systems\, focusing on the set of Birkhoff sums along periodic or
 bits. We begin by characterizing when the Birkhoff spectrum of a Hölder c
 ontinuous observable on a basic set is dense in the real line\, showing th
 at dispersion and non-arithmeticity are key conditions. Our first main rig
 idity result states that boundedness of the spectrum forces the observable
  to be cohomologous to zero—extending the classical Livsic theorem. We f
 urther prove that if the spectrum is contained in a finite union of arithm
 etic progressions\, the observable must be arithmetic\, and for Anosov dif
 feomorphisms\, cohomologous to a constant.\nThese results are then extende
 d to continuous-time systems\, including Anosov flows and geodesic flows o
 n Anosov manifolds.\n\n//indico.ictp.it/event/11488/
LOCATION:ICTP Leonardo Building - Luigi Stasi Seminar Room
URL://indico.ictp.it/event/11488/
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