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UID:8976@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260120T110000
DTEND;TZID=Europe/Paris:20260120T120000
DTSTAMP:20260116T095426Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-287/
SUMMARY:Albert Fisher (Univ São Paulo): Finite and infinite  invariant mea
 sures for adic transformations
DESCRIPTION:Albert Fisher: We will describe a new paper with Marina Talet o
 f Aix-Marseille University\, in which we classify the invariant Borel meas
 ures for adic transformations.\n\nWe restrict to finite rank (bounded alph
 abet size) and we assume the measure is finite on the path space of some s
 ub-Bratteli diagram defined by erasing vertices or edges.\n\nVershik's adi
 c transformations generalize the classical Kakutani-von Neumann odometer m
 ap\, but go far beyond that example as they can be used to model for examp
 le irrational circle rotations\, interval exchange transformations\, subst
 itution dynamical systems\, and cutting-and-stacking constructions.\n\nThe
  first generalization beyond the odometer is to a primitive nonnegative in
 teger matrix $M$ which defines a subshift of finite type\, with the adic t
 ransformation acting transversally to the shift map. In contrast to the sh
 ift map\, these are uniquely ergodic\, minimal and of zero entropy.\n\nThi
 ngs get much more interesting when one allows for a matrix sequence (a non
 stationary adic transformation)\, for the nonprimitive case\, and for infi
 nite measures.\n\nTo classify these maps we extend the approach of Bezugly
 i\, Kwiatkowski\, Medynets and Solomyak for the nonprimitive stationary ca
 se to the nonprimitive nonstationary case\, allowing for measures which ma
 y be locally infinite. We give a necessary and sufficient condition for th
 e measure to be infinite. To carry this out we prove a nonstationary versi
 on of the Frobenius-Victory Theorem.\n\nAs an application of our general r
 esult\, we introduce nested irrational rotations\, giving a checkable cond
 ition for the tower measure to be infinite.\n\nSee arXiv:2510.13071 [math.
 DS]
CATEGORIES:Séminaire,Ernest
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
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 e de Séminaire 304-306 (3ème étage):geo:0,0
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