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SUMMARY:Célia Cisternino (University of Liège)
DTSTART:20200526T123000Z
DTEND:20200526T133000Z
DTSTAMP:20260423T021226Z
UID:OWNS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/4/">Erg
 odic behavior of transformations associated with alternate base expansions
 </a>\nby Célia Cisternino (University of Liège) as part of One World Num
 eration seminar\n\n\nAbstract\nWe consider a p-tuple of real numbers great
 er than 1\, $\\boldsymbol{\\beta} = (\\beta_1\,\\dots\,\\beta_p)$\, called
  an alternate base\, to represent real numbers. Since these representation
 s generalize the 𝛽-representation introduced by Rényi in 1958\, a lot 
 of questions arise. In this talk\, we will study the transformation genera
 ting the alternate base expansions (greedy representations). First\, we wi
 ll compare the $\\boldsymbol{\\beta}$-expansion and the $(\\beta_1*\\cdots
 *\\beta_p)$-expansion over a particular digit set and study the cases when
  the equality holds. Next\, we will talk about the existence of a measure 
 equivalent to Lebesgue\, invariant for the transformation corresponding to
  the alternate base and also about the ergodicity of this transformation. 
 \n\nThis is a joint work with Émilie Charlier and Karma Dajani.\n
LOCATION:https://researchseminars.org/talk/OWNS/4/
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