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SUMMARY:Positivity of the Lyapunov exponent for potentials generated by hy
 perbolic transformations
DTSTART:20210507T141500
DTSTAMP:20260427T213051Z
UID:c045b14503c4669acdb9bccb41f5fadda7ac2d3a11db8d9f9942c751
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Zhenghe Zhang\, UC Riverside\nAbstract: In this talk\, I
  will introduce a recent work in showing positivity of the Lyapunov expone
 nt for Schr\\"odinger operators with potentials generated by hyperbolic dy
 namics. Specifically\, we showed that if the base dynamics is a subshift o
 f finite type with an ergodic measure admitting a local product structure 
 and if it has a fixed point\, then for all nonconstant H\\"older continuou
 s potentials\, the set of energies with zero Lyapunov exponent is a discre
 te set. If the potentials are locally constant or globally fiber bunched\,
  then the set of zero Lyapunov exponent is finite. We also showed that for
  generic such potentials\, we have full positivity in the general case and
  uniform positivity in the special cases. Such hyperbolic dynamics include
  expanding maps such as the doubling map on the unit circle\, or  Anosov 
 diffeomorphism such as the Arnold's Cat map on 2-dimensional torus. It can
  also be applied to Markov chains whose special cases include the i.i.d. r
 andom variable. This is a joint with A. Avila and D. Damanik. (This talk b
 uilds on last week's talk by D. Damanik.)
LOCATION:https://epfl.zoom.us/j/64376837572?pwd=Q1dFbGROU3VqM2dvOGdGWFFHZE
 NQQT09
STATUS:CONFIRMED
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