scholarly journals On–off intermittency and chaotic walks

2019 ◽  
Vol 40 (7) ◽  
pp. 1805-1842
Author(s):  
ALE JAN HOMBURG ◽  
VAHATRA RABODONANDRIANANDRAINA
Keyword(s):  
Lyapunov Exponent ◽  
Random Walks ◽  
The Other ◽  
Skew Product ◽  
End Points ◽  
Interval Maps ◽  
Markov Random ◽  
Doubling Map ◽  
Product Maps ◽  
Equivalent Description

We consider a class of skew product maps of interval diffeomorphisms over the doubling map. The interval maps fix the end points of the interval. It is assumed that the system has zero fiber Lyapunov exponent at one endpoint and zero or positive fiber Lyapunov exponent at the other endpoint. We prove the appearance of on–off intermittency. This is done using the equivalent description of chaotic walks: random walks driven by the doubling map. The analysis further relies on approximating the chaotic walks by Markov random walks, that are constructed using Markov partitions for the doubling map.

Parabolic invariant tori in quasi-periodically forced skew-product maps

2021 ◽  
Vol 277 ◽  
pp. 234-274
Author(s):  
Xinyu Guan ◽  
Jianguo Si ◽  
Wen Si
Keyword(s):  
Invariant Tori ◽  
Skew Product ◽  
Product Maps

Bayesian Comparison of Two Regression Lines

1978 ◽  
Vol 3 (2) ◽  
pp. 179-188
Author(s):  
Robert K. Tsutakawa
Keyword(s):  
Posterior Distribution ◽  
Prior Distribution ◽  
Posterior Probability ◽  
Finite Interval ◽  
Regression Line ◽  
The Other ◽  
End Points ◽  
Independent Variable

The comparison of two regression lines is often meaningful or of interest over a finite interval I of the independent variable. When the prior distribution of the parameters is a natural conjugate, the posterior distribution of the distances between two regression lines at the end points of I is bivariate t. The posterior probability that one regression line lies above the other uniformly over I is numerically evaluated using this distribution.

A note on a problem on ω-limit sets ofN–dimensional skew-product maps

2010 ◽  
Vol 87 (6) ◽  
pp. 1228-1232
Author(s):  
Juan Luis García Guirao ◽  
Fernando López Pelayo
Keyword(s):  
Skew Product ◽  
Limit Sets ◽  
Product Maps

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

A simple random walk on parallel axes moving at different rates

1975 ◽  
Vol 12 (03) ◽  
pp. 466-476
Author(s):  
V. Barnett
Keyword(s):  
Random Walk ◽  
Simple Random Walk ◽  
Time Instant ◽  
Packed Columns ◽  
The Other ◽  
End Points ◽  
Previous Time ◽  
The Right

Prompted by a rivulet model for the flow of liquid through packed columns we consider a simple random walk on parallel axes moving at different rates. A particle may make one of three transitions at each time instant: to the right or to the left on the axis it was on at the previous time instant, or across to the other axis. Results are obtained for the unrestricted walk, and for the walk with absorbing, or reflecting, end-points.

scholarly journals Circle diffeomorphisms forced by expanding circle maps

2011 ◽  
Vol 32 (6) ◽  
pp. 2011-2024 ◽  
Author(s):  
ALE JAN HOMBURG
Keyword(s):  
Natural Extension ◽  
Skew Product ◽  
Circle Maps ◽  
Expanding Circle ◽  
Topologically Mixing ◽  
Almost All ◽  
Open Class ◽  
Product Maps ◽  
Circle Diffeomorphisms

AbstractWe discuss the dynamics of skew product maps defined by circle diffeomorphisms forced by expanding circle maps. We construct an open class of such systems that are robustly topologically mixing and for which almost all points in the same fiber converge under iteration. This property follows from the construction of an invariant attracting graph in the natural extension, a skew product of circle diffeomorphisms forced by a solenoid homeomorphism.

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