On the abundance of traveling waves in coupled expanding circle maps

2000 ◽  
pp. 15-21 ◽  
Author(s):  
V. Afraimovich ◽  
M. Courbage
Keyword(s):  
Traveling Waves ◽  
Circle Maps ◽  
Expanding Circle

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.

ABUNDANCE OF TRAVELING WAVES IN COUPLED CIRCLE MAPS

2000 ◽  
Vol 10 (09) ◽  
pp. 2061-2073 ◽  
Author(s):  
WEN-XIN QIN
Keyword(s):  
Fixed Point ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Initial Conditions ◽  
Periodic Structures ◽  
Time Evolution Operator ◽  
Circle Maps ◽  
Temporal Complexity ◽  
Spatial Periodicity ◽  
The Stability

In this paper we study the existence of traveling waves with any rational velocity in coupled circle maps. We introduce an induced map, then a traveling wave with velocity p/q corresponds to a fixed point of the induced map. Moreover, the stability of a traveling wave is equivalent to that of the corresponding fixed point. Space translational system is chaotic on the set of traveling waves with rational velocities. In addition, time evolution operator exhibits sensitivity-like behavior with respect to initial conditions. By investigating the spatial periodicity of traveling waves, we obtain infinitely many space-time periodic structures. We also consider spatial asymptoticity of these traveling waves, which leads to the existence of fronts, defect solutions and soliton-like solutions. The abundance of traveling waves may be regarded as a signature of the spatial-temporal complexity in extended systems.

scholarly journals Eigenfunctions for smooth expanding circle maps

Nonlinearity ◽  
2004 ◽  
Vol 17 (5) ◽  
pp. 1723-1730 ◽  
Author(s):  
Gerhard Keller ◽  
Hans Henrik Rugh
Keyword(s):  
Circle Maps ◽  
Expanding Circle

scholarly journals Mean-Field Coupling of Identical Expanding Circle Maps

2016 ◽  
Vol 164 (4) ◽  
pp. 858-889 ◽  
Author(s):  
Fanni Sélley ◽  
Péter Bálint
Keyword(s):  
Mean Field ◽  
Circle Maps ◽  
Field Coupling ◽  
Expanding Circle

scholarly journals Analytic expanding circle maps with explicit spectra

Nonlinearity ◽  
2013 ◽  
Vol 26 (12) ◽  
pp. 3231-3245 ◽  
Author(s):  
Julia Slipantschuk ◽  
Oscar F Bandtlow ◽  
Wolfram Just
Keyword(s):  
Circle Maps ◽  
Expanding Circle

Power-law persistence characterizes traveling waves in coupled circle maps with repulsive coupling

2007 ◽  
Vol 75 (6) ◽  
Author(s):  
Prashant M. Gade ◽  
D. V. Senthilkumar ◽  
Sukratu Barve ◽  
Sudeshna Sinha
Keyword(s):  
Power Law ◽  
Traveling Waves ◽  
Circle Maps

scholarly journals On stochastic stability of expanding circle maps with neutral fixed points

2013 ◽  
Vol 28 (3) ◽  
pp. 423-452 ◽  
Author(s):  
Weixiao Shen ◽  
Sebastian van Strien
Keyword(s):  
Fixed Points ◽  
Stochastic Stability ◽  
Circle Maps ◽  
Expanding Circle

scholarly journals Lower bounds for the Ruelle spectrum of analytic expanding circle maps

2017 ◽  
Vol 39 (2) ◽  
pp. 289-310 ◽  
Author(s):  
OSCAR F. BANDTLOW ◽  
FRÉDÉRIC NAUD
Keyword(s):  
Lower Bounds ◽  
Blaschke Products ◽  
Expanding Maps ◽  
Circle Maps ◽  
Expanding Circle ◽  
Dense Set

We prove that there exists a dense set of analytic expanding maps of the circle for which the Ruelle eigenvalues enjoy exponential lower bounds. The proof combines potential theoretic techniques and explicit calculations for the spectrum of expanding Blaschke products.

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