BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Katrin Gelfert (UFRJ) DTSTART:20201113T101500Z DTEND:20201113T104500Z DTSTAMP:20260423T021929Z UID:DSSUJ/18 DESCRIPTION:Title: H eterodimensionality of skew-products with concave fiber maps\nby Katri n Gelfert (UFRJ) as part of Dynamical systems seminar at the Jagiellonian University\n\nLecture held in 1016.\n\nAbstract\nI will present some examp les of skew-products with concave\ninterval fiber maps over a certain subs hift. Here the subshift occurs\nas the projection of those orbits that sta y in a given neighborhood\nand gives rise to a new type of symbolic space which is (essentially)\ncoded. The fiber maps have expanding and contracti ng regions. As a\nconsequence\, the skew-product dynamics has pairs of hor seshoes of\ndifferent type of hyperbolicity. In some cases\, they dynamica lly\ninteract due to the superimposed effects of the (fiber) contraction\n and expansion\, leading to nonhyperbolic dynamics that is reflected on\nth e ergodic level (existence of nonhyperbolic ergodic measures). The\nspace of ergodic measures of the shift space is shown to be an\nentropy-dense Po ulsen simplex\, ergodic measures lift canonically to\nergodic measures for the skew-product.\nSuch skew-products can be embedded in increasing entro py one-parameter\nfamily of diffeomorphisms which stretch from a heterodim ensional cycle\nto a collision of homoclinic classes. I will discuss some ingredients\nof associated bifurcation phenomena that involve a jump of th e space\nof ergodic measures and\, in some cases\, also of entropy. (Joint work\nwith L.J.Díaz and M.Rams)\n LOCATION:https://researchseminars.org/talk/DSSUJ/18/ END:VEVENT END:VCALENDAR