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Extreme Value Laws in Dynamical Systems for Non-smooth Observations

Title
Extreme Value Laws in Dynamical Systems for Non-smooth Observations
Type
Article in International Scientific Journal
Year
2011
Authors
Ana Cristina M Moreira Freitas
(Author)
FEP
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Mike Todd
(Author)
Other
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Journal
Vol. 142
Pages: 108-126
ISSN: 0022-4715
Publisher: Springer Nature
Indexing
Scientific classification
FOS: Natural sciences > Physical sciences
Other information
Authenticus ID: P-002-XVC
Abstract (EN): We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue. This is a counterpart to the result of the authors in the absolutely continuous case. Moreover, we prove an equivalent result for returns to dynamically defined cylinders. This allows us to show that we have Extreme Value Laws for various dynamical systems with equilibrium states with good mixing properties. In order to achieve these goals we tailor our observables to the form of the measure at hand.
Language: English
Type (Professor's evaluation): Scientific
Contact: amoreira@fep.up.pt; jmfreita@fc.up.pt; mtodd@math.bu.edu
No. of pages: 19
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