scholarly journals An algorithm to compute rotation intervals of circle maps

2021 ◽  
pp. 105915
Author(s):  
Lluís Alsedà ◽  
Salvador Borrós-Cullell
Keyword(s):  
Circle Maps

GENERALIZED SYNCHRONIZATION, FREQUENCY-LOCKING AND PHASE-LOCKING OF COUPLED SINE CIRCLE MAPS

2001 ◽  
Vol 11 (08) ◽  
pp. 2245-2253
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Invariant Manifold ◽  
Coupling Strength ◽  
Phase Locking ◽  
Coupled System ◽  
Generalized Synchronization ◽  
Frequency Locking ◽  
Local Systems ◽  
Circle Maps ◽  
The Individual

Applying invariant manifold theorem, we study the existence of generalized synchronization of a coupled system, with local systems being different sine circle maps. We specify a range of parameters for which the coupled system achieves generalized synchronization. We also investigate the relation between generalized synchronization, predictability and equivalence of dynamical systems. If the parameters are restricted in the specified range, then all the subsystems are topologically equivalent, and each subsystem is predictable from any other subsystem. Moreover, these subsystems are frequency locked even if the frequencies are greatly different in the absence of coupling. If the local systems are identical without coupling, then the widths of the phase-locked intervals of the coupled system are the same as those of the individual map and are independent of the coupling strength.

SIMPLE AND COMPLEX DYNAMICS FOR ONE-DIMENSIONAL MANIFOLD MAPS

1995 ◽  
Vol 05 (05) ◽  
pp. 1351-1355
Author(s):  
VLADIMIR FEDORENKO
Keyword(s):  
Topological Entropy ◽  
Complex Dynamics ◽  
Periodic Points ◽  
Dimensional Manifold ◽  
One Dimensional ◽  
Circle Maps ◽  
Interval Maps ◽  
Chain Recurrent Set ◽  
Recurrent Set

We give a characterization of complex and simple interval maps and circle maps (in the sense of positive or zero topological entropy respectively), formulated in terms of the description of the dynamics of the map on its chain recurrent set. We also describe the behavior of complex maps on their periodic points.

A SRB-measure for globally coupled circle maps

Nonlinearity ◽  
1997 ◽  
Vol 10 (6) ◽  
pp. 1435-1469 ◽  
Author(s):  
Esa Järvenpää
Keyword(s):  
Srb Measure ◽  
Circle Maps

scholarly journals Robust local Hölder rigidity of circle maps with breaks

2018 ◽  
Vol 35 (7) ◽  
pp. 1827-1845 ◽  
Author(s):  
Konstantin Khanin ◽  
Saša Kocić
Keyword(s):  
Circle Maps

Circle maps with symmetry-breaking perturbations

1992 ◽  
Vol 57 (1-2) ◽  
pp. 58-84 ◽  
Author(s):  
Anders B. Eriksson ◽  
Torbjörn Einarsson ◽  
Stellan Östlund
Keyword(s):  
Symmetry Breaking ◽  
Circle Maps

scholarly journals The Rigidity Problem for Analytic Critical Circle Maps

2006 ◽  
Vol 6 (2) ◽  
pp. 317-351 ◽  
Author(s):  
D. Khmelev ◽  
M. Yampolsky
Keyword(s):  
Circle Maps ◽  
Critical Circle

scholarly journals ROTATION SETS FOR ORBITS OF DEGREE ONE CIRCLE MAPS

2002 ◽  
Vol 12 (02) ◽  
pp. 429-437
Author(s):  
LLUÍS ALSEDÀ ◽  
FRANCESC MAÑOSAS ◽  
MOIRA CHAS
Keyword(s):  
Circle Map ◽  
Circle Maps ◽  
Rotation Interval ◽  
The One ◽  
Rotation Set ◽  
Dynamical Information

Let F be the lifting of a circle map of degree one. In [Bamón et al., 1984] a notion of F-rotation interval of a point [Formula: see text] was given. In this paper we define and study a new notion of a rotation set of point which preserves more of the dynamical information contained in the sequences [Formula: see text] than the one preserved from [Bamón et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bamón et al., 1984] in our settings.

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