scholarly journals Quantitative recurrence for generic homeomorphisms

2017 ◽  
Vol 145 (11) ◽  
pp. 4751-4761 ◽  
Author(s):  
André Junqueira
Keyword(s):  
Quantitative Recurrence

scholarly journals Quantitative recurrence properties for beta-dynamical system

2011 ◽  
Vol 228 (4) ◽  
pp. 2071-2097 ◽  
Author(s):  
Bo Tan ◽  
Bao-Wei Wang
Keyword(s):  
Dynamical System ◽  
Quantitative Recurrence

Quantitative recurrence properties for group actions

Nonlinearity ◽  
2008 ◽  
Vol 22 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Dong Han Kim
Keyword(s):  
Group Actions ◽  
Quantitative Recurrence

scholarly journals A large deviations bound for the Teichmüller flow on the moduli space of abelian differentials

2010 ◽  
Vol 31 (4) ◽  
pp. 1043-1071 ◽  
Author(s):  
VÍTOR ARAÚJO ◽  
ALEXANDER I. BUFETOV
Keyword(s):  
Dynamical Systems ◽  
Large Deviations ◽  
Moduli Space ◽  
Geodesic Flow ◽  
Large Deviation ◽  
Suspension Flows ◽  
Abelian Differentials ◽  
Quantitative Recurrence ◽  
Teichmuller Geodesic Flow ◽  
Teichmüller Flow

AbstractLarge deviation rates are obtained for suspension flows over symbolic dynamical systems with a countable alphabet. We use a method employed previously by the first author [Large deviations bound for semiflows over a non-uniformly expanding base. Bull. Braz. Math. Soc. (N.S.)38(3) (2007), 335–376], which follows that of Young [Some large deviation results for dynamical systems. Trans. Amer. Math. Soc.318(2) (1990), 525–543]. As a corollary of the main results, we obtain a large deviation bound for the Teichmüller flow on the moduli space of abelian differentials, extending earlier work of Athreya [Quantitative recurrence and large deviations for Teichmuller geodesic flow. Geom. Dedicata119 (2006), 121–140].

scholarly journals Quantitative recurrence for free semigroup actions

Nonlinearity ◽  
2018 ◽  
Vol 31 (3) ◽  
pp. 864-886 ◽  
Author(s):  
Maria Carvalho ◽  
Fagner B Rodrigues ◽  
Paulo Varandas
Keyword(s):  
Free Semigroup ◽  
Semigroup Actions ◽  
Quantitative Recurrence

scholarly journals Quantitative recurrence results for random walks

2018 ◽  
Vol 18 (03) ◽  
pp. 1850003
Author(s):  
Nuno Luzia
Keyword(s):  
Random Walk ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Central Limit ◽  
Lattice Random Walks ◽  
Asymptotic Number ◽  
Quantitative Recurrence ◽  
Recurrence Theorem ◽  
Local Central Limit Theorem

First, we prove an almost sure local central limit theorem for lattice random walks in the plane. The corresponding version for random walks in the line has been considered previously by the author. This gives us an extension of Pólya’s Recurrence Theorem, namely we consider an appropriate subsequence of the random walk and give the asymptotic number of returns to the origin and other states. Secondly, we prove an almost sure local central limit theorem for (not necessarily lattice) random walks in the line or in the plane, which will also give us quantitative recurrence results. Finally, we prove a version of the almost sure central limit theorem for multidimensional random walks. This is done by exploiting a technique developed by the author.

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