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SUMMARY:The Fibonacci Hamiltonian - Gorodetski\, A (University of Californ
 ia\, Irvine)
DTSTART:20150410T123000Z
DTEND:20150410T133000Z
UID:TALK58847@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: David Damanik (Rice University)\, William Yessen (
 Rice University) \n\nIn the talk we will consider the discrete Schrodinger
  operator with potential given by the Fibonacci substitution sequence (the
  Fibonacci Hamiltonian) and provide a detailed description of its spectrum
  and spectral characteristics (namely\, the optimal Holder exponent of the
  integrated density of states\, the dimension of the density of states mea
 sure\, the dimension of the spectrum\, and the upper transport exponent) f
 or all values of the coupling constant. In particular\, we will establish 
 strict inequalities between the four spectral characteristics in question\
 , and discuss the exact small and large coupling asymptotics of these spec
 tral characteristics. A crucial ingredient is the relation between spectra
 l properties of the Fibonacci Hamiltonian and dynamical properties of the 
 Fibonacci trace map (such as dimensional characteristics of the non-wander
 ing hyperbolic set and its measure of maximal entropy as well as other equ
 ilibrium measures\, topological entropy\, multipliers of periodic orbits).
  We will establish exact identities relating the spectral and dynamical qu
 antities\, and show the connection between the spectral quantities and the
  thermodynamic pressure function. \n
LOCATION:Seminar Room 1\, Newton Institute
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