Thesis etd-05042018-143921 |
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Thesis type
Tesi di dottorato di ricerca
URN
etd-05042018-143921
Thesis title
Spectral Gap for Contracting Fiber Systems and Applications
Academic discipline
MAT/01 - LOGICA MATEMATICA
Course of study
SCIENZE DI BASE
Supervisors
.
tutor Prof. Galatolo, Stefano
tutor Prof.ssa Pacifico, Maria José
tutor Prof.ssa Pacifico, Maria José
Keywords
- dynamical systems
- ergodic theory
- Lorenz
- spectral Gap
- stability
Graduation session start date
07/10/2015
Availability
Full
Abstract (Inglese)
Abstract (Italiano)
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) ).
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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| tese_RAF..._2015.pdf | 548.80 Kb |
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