scholarly journals Transfer Operators and Limit Laws for Typical Cocycles

2022 ◽  
Author(s):  
Kiho Park ◽  
Mark Piraino
Keyword(s):  
Limit Laws ◽  
Transfer Operators

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

scholarly journals On Gibbs Measures and Spectra of Ruelle Transfer Operators

2017 ◽  
Vol 60 (2) ◽  
pp. 411-421
Author(s):  
Luchezar Stoyanov
Keyword(s):  
Spectral Radius ◽  
Spectral Properties ◽  
Gibbs Measures ◽  
Transfer Operator ◽  
Frobenius Theorem ◽  
Transfer Operators

AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.

scholarly journals On Sinaĭ Billiards on Flat Surfaces with Horns

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
Henk Bruin
Keyword(s):  
Exponential Decay ◽  
Height Function ◽  
Suspension Flow ◽  
Limit Laws ◽  
Suspension Flows ◽  
Flat Surfaces ◽  
Exponential Tails ◽  
Exponential Decay Of Correlations ◽  
Sinai Billiards ◽  
Young Towers

AbstractWe show that certain billiard flows on planar billiard tables with horns can be modeled as suspension flows over Young towers (Ann. Math. 147:585–650, 1998) with exponential tails. This implies exponential decay of correlations for the billiard map. Because the height function of the suspension flow itself is polynomial when the horns are Torricelli-like trumpets, one can derive Limit Laws for the billiard flow, including Stable Limits if the parameter of the Torricelli trumpet is chosen in (1, 2).

scholarly journals SYNCHRONIZATION AS A PROCESS OF SHARING AND TRANSFERRING INFORMATION

2012 ◽  
Vol 22 (11) ◽  
pp. 1250261 ◽  
Author(s):  
ERIK M. BOLLT
Keyword(s):  
Symbolic Dynamics ◽  
Slow Manifold ◽  
Transfer Entropy ◽  
The Other ◽  
Chaotic Oscillators ◽  
Smale Horseshoe ◽  
Global System ◽  
Identity Function ◽  
Transfer Operators ◽  
First Time

Synchronization of chaotic oscillators has become well characterized by errors which shrink relative to a synchronization manifold. This manifold is the identity function in the case of identical systems, or some other slow manifold in the case of generalized synchronizaton in the case of nonidentical components. On the other hand, since many decades beginning with the Smale horseshoe, chaotic oscillators can be well understood in terms of symbolic dynamics as information producing processes. We study here the synchronization of a pair of chaotic oscillators as a process for sharing information bearing bits transferred between each other, by measuring the transfer entropy tracked as the global system transitions to the synchronization state. Further, we present for the first time the notion of transfer entropy in the measure theoretic setting of transfer operators.

scholarly journals Second-order limit laws for occupation times of fractional Brownian motion

2017 ◽  
Vol 54 (2) ◽  
pp. 444-461 ◽  
Author(s):  
Fangjun Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Method Of Moments ◽  
Second Order ◽  
Hurst Index ◽  
Occupation Times ◽  
Limit Laws ◽  
Additive Functionals ◽  
Finite Dimensional ◽  
Functional Version

Abstract We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1 / d, using the method of moments and extending the Kallianpur–Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

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