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Tesi etd-05042018-143921


Tipo di tesi
Tesi di dottorato di ricerca
Autore
NOBREGA DE OLIVEIRA LUCENA, RAFAEL
URN
etd-05042018-143921
Titolo
Spectral Gap for Contracting Fiber Systems and Applications
Settore scientifico disciplinare
MAT/01
Corso di studi
SCIENZE DI BASE
Relatori
tutor Prof. Galatolo, Stefano
tutor Prof.ssa Pacifico, Maria José
Parole chiave
  • dynamical systems
  • ergodic theory
  • Lorenz
  • spectral Gap
  • stability
Data inizio appello
07/10/2015
Consultabilità
Completa
Riassunto
We consider transformations preserving a contracting foliation, such that the associated quotient map satis es a Lasota Yorke inequality. We prove that the associated transfer operator, acting on suitable normed spaces,has spectral gap.

As an application we consider Lorenz-Like two dimensional maps (piecewise hyperbolic with unbounded contraction and expansion rate): we prove that those systems have spectral gap and we show a quantitative estimation for their statistical stability. Under deterministic perturbations of the system, the physical measure varies continuously, with a modulus of continuity O(delta log (delta) ).
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