The role of periodic orbits in semiclassical quantization

2006 ◽  
pp. 293-298 ◽  
Author(s):  
Michael Tabor
Keyword(s):  
Periodic Orbits ◽  
Semiclassical Quantization

On-Off Intermittency and Riddled Basins of Attraction in a Coupled Map System

1998 ◽  
Vol 01 (02n03) ◽  
pp. 161-180 ◽  
Author(s):  
J. Laugesen ◽  
E. Mosekilde ◽  
Yu. L. Maistrenko ◽  
V. L. Maistrenko
Keyword(s):  
Periodic Orbits ◽  
Basin Of Attraction ◽  
Basins Of Attraction ◽  
Chaotic State ◽  
One Dimensional ◽  
Type Iii ◽  
Different Types ◽  
One Dimensional Maps ◽  
The Basin Of Attraction

The paper examines the appearance of on-off intermittency and riddled basins of attraction in a system of two coupled one-dimensional maps, each displaying type-III intermittency. The bifurcation curves for the transverse destablilization of low periodic orbits embeded in the synchronized chaotic state are obtained. Different types of riddling bifurcation are discussed, and we show how the existence of an absorbing area inside the basin of attraction can account for the distinction between local and global riddling as well as for the distinction between hysteric and non-hysteric blowout. We also discuss the role of the so-called mixed absorbing area that exists immediately after a soft riddling bifurcation. Finally, we study the on-off intermittency that is observed after a non-hysteric blowout bifurcaton.

Periodic orbits and semiclassical quantization of dispersing billiards

1992 ◽  
Vol 25 (17) ◽  
pp. 4595-4611 ◽  
Author(s):  
T Harayama ◽  
A Shudo
Keyword(s):  
Periodic Orbits ◽  
Semiclassical Quantization ◽  
Dispersing Billiards

Role of unstable periodic orbits in bubbling weak generalized synchronization

2020 ◽  
Vol 414 ◽  
pp. 132678
Author(s):  
Noi Takahashi ◽  
Satoru Tsugawa
Keyword(s):  
Periodic Orbits ◽  
Generalized Synchronization ◽  
Unstable Periodic Orbits

scholarly journals Intermittent chaos driven by nonlinear Alfvén waves

2004 ◽  
Vol 11 (5/6) ◽  
pp. 691-700 ◽  
Author(s):  
E. L. Rempel ◽  
A. C.-L. Chian ◽  
A. J. Preto ◽  
S. Stephany
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Systems Approach ◽  
Alfven Waves ◽  
Space Plasmas ◽  
Alfvén Waves ◽  
Unstable Periodic Orbits ◽  
Phase Dynamics ◽  
Intermittent Chaos

Abstract. We investigate the relevance of chaotic saddles and unstable periodic orbits at the onset of intermittent chaos in the phase dynamics of nonlinear Alfvén waves by using the Kuramoto-Sivashinsky (KS) equation as a model for phase dynamics. We focus on the role of nonattracting chaotic solutions of the KS equation, known as chaotic saddles, in the transition from weak chaos to strong chaos via an interior crisis and show how two of these unstable chaotic saddles can interact to produce the plasma intermittency observed in the strongly chaotic regimes. The dynamical systems approach discussed in this work can lead to a better understanding of the mechanisms responsible for the phenomena of intermittency in space plasmas.

Role of Nonperiodic Orbits in the Semiclassical Quantization of the Truncated Hyperbola Billiard

1995 ◽  
Vol 74 (22) ◽  
pp. 4408-4411 ◽  
Author(s):  
R. Aurich ◽  
T. Hesse ◽  
F. Steiner
Keyword(s):  
Semiclassical Quantization

scholarly journals Pattern recognition using chaotic neural networks

1998 ◽  
Vol 2 (4) ◽  
pp. 243-247 ◽  
Author(s):  
Z. Tan ◽  
B. S. Hepburn ◽  
C. Tucker ◽  
M. K. Ali
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Pattern Recognition ◽  
Dynamical Systems ◽  
Periodic Orbits ◽  
Basins Of Attraction ◽  
Limited Information ◽  
Unstable Periodic Orbits ◽  
Chaotic Neural Networks

Pattern recognition by chaotic neural networks is studied using a hyperchaotic neural network as model. Virtual basins of attraction are introduced around unstable periodic orbits which are then used as patterns. Search for periodic orbits in dynamical systems is treated as a process of pattern recognition. The role of synapses on patterns in chaotic networks is discussed. It is shown that distorted states having only limited information of the patterns are successfully recognized.

scholarly journals Role of unstable periodic orbits in phase transitions of coupled map lattices

2007 ◽  
Vol 75 (3) ◽  
Author(s):  
Kazumasa Takeuchi ◽  
Masaki Sano
Keyword(s):  
Phase Transitions ◽  
Periodic Orbits ◽  
Coupled Map Lattices ◽  
Unstable Periodic Orbits

Role of unstable periodic orbits in phase and lag synchronization between coupled chaotic oscillators

2003 ◽  
Vol 13 (1) ◽  
pp. 309-318 ◽  
Author(s):  
Diego Pazó ◽  
Michael A. Zaks ◽  
Jürgen Kurths
Keyword(s):  
Periodic Orbits ◽  
Unstable Periodic Orbits ◽  
Lag Synchronization ◽  
Chaotic Oscillators

The rectilinear three-body problem using symbol sequence II: role of the periodic orbits

2009 ◽  
Vol 103 (3) ◽  
pp. 191-207 ◽  
Author(s):  
Masaya Masayoshi Saito ◽  
Kiyotaka Tanikawa
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Three Body Problem ◽  
Symbol Sequence ◽  
Three Body
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