scholarly journals Topological Pressure for One-Dimensional Holomorphic Dynamical Systems

2007 ◽  
Vol 55 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Katrin Gelfert ◽  
Christian Wolf
Keyword(s):  
Dynamical Systems ◽  
Topological Pressure ◽  
One Dimensional

VARIATIONAL PRINCIPLE FOR SUBADDITIVE SEQUENCE OF POTENTIALS IN BUNDLE RANDOM DYNAMICAL SYSTEMS

2009 ◽  
Vol 09 (02) ◽  
pp. 205-215 ◽  
Author(s):  
XIANFENG MA ◽  
ERCAI CHEN
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Multifractal Analysis ◽  
Weak Condition ◽  
Random Dynamical Systems ◽  
Topological Pressure ◽  
Set Up

The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in the study of multifractal analysis for random version of nonconformal dynamical systems.

scholarly journals Ultradiscrete bifurcations for one dimensional dynamical systems

2020 ◽  
Vol 61 (12) ◽  
pp. 122702
Author(s):  
Shousuke Ohmori ◽  
Yoshihiro Yamazaki
Keyword(s):  
Dynamical Systems ◽  
One Dimensional

From Dispersion to Laminarity in Dynamical Systems

1994 ◽  
Vol 49 (12) ◽  
pp. 1241-1247 ◽  
Author(s):  
G. Zumofen ◽  
J. Klafter
Keyword(s):  
Random Walk ◽  
Dynamical Systems ◽  
Continuous Time ◽  
Chaotic Behavior ◽  
Continuous Time Random Walk ◽  
Standard Map ◽  
One Dimensional ◽  
Enhanced Diffusion

Abstract We study transport in dynamical systems characterized by intermittent chaotic behavior with coexistence of dispersive motion due to periods of localization, and of enhanced diffusion due to periods of laminar motion. This transport is discussed within the continuous-time random walk approach which applies to both dispersive and enhanced motions. We analyze the coexistence for the standard map and for a one-dimensional map.

scholarly journals Subadditive Pre-Image Variational Principle for Bundle Random Dynamical Systems

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 309
Author(s):  
Xianfeng Ma ◽  
Zhongyue Wang ◽  
Hailin Tan
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Random Dynamical Systems ◽  
Topological Pressure ◽  
Image Measure ◽  
Measure Preserving Transformations

A central role in the variational principle of the measure preserving transformations is played by the topological pressure. We introduce subadditive pre-image topological pressure and pre-image measure-theoretic entropy properly for the random bundle transformations on a class of measurable subsets. On the basis of these notions, we are able to complete the subadditive pre-image variational principle under relatively weak conditions for the bundle random dynamical systems.

Application of a Generalized Frobenius-Perron Operator Scheme to Multivariate Nonlinear Dynamical Systems

1995 ◽  
Vol 50 (12) ◽  
pp. 1123-1127
Author(s):  
R. Stoop ◽  
W.-H. Steeb
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Free Energies ◽  
Nonlinear Dynamical ◽  
One Dimensional ◽  
One Dimensional Maps ◽  
Operator Scheme

Abstract The concept of generalized Frobenius-Perron operators is applied to multivariante nonlinear dynamical systems, and the associated generalized free energies are investigated. As important applications, diffusion-related free energies obtained from normally and superlinearly diffusive one-dimensional maps are discussed.

UNIFORMITY AND SPATIAL CHAOS OF SPATIAL PHYSICS KINEMATIC SYSTEM

2010 ◽  
Vol 24 (28) ◽  
pp. 5495-5503
Author(s):  
SHUTANG LIU ◽  
FUYAN SUN ◽  
JIE SUN
Keyword(s):  
Dynamical Systems ◽  
Lattice Model ◽  
Nonlinear Dynamical Systems ◽  
Coupled Map Lattice ◽  
Nonlinear Dynamical ◽  
One Dimensional ◽  
Uniform System ◽  
Spatial Chaos ◽  
Kinematic System ◽  
Bifurcation Behavior

This article summarizes the uniformity law of spatial physics kinematic systems, and studies the chaos and bifurcation behavior of the uniform system in space. In particular, it also fully explains the relation among the uniform system, the coupled map lattice model which has attracted considerable interest currently, and one-dimensional nonlinear dynamical systems.

PERIOD-DOUBLING SCENARIO WITHOUT FLIP BIFURCATIONS IN A ONE-DIMENSIONAL MAP

2005 ◽  
Vol 15 (04) ◽  
pp. 1267-1284 ◽  
Author(s):  
V. AVRUTIN ◽  
M. SCHANZ
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Period Doubling ◽  
Pitchfork Bifurcation ◽  
Period Doubling Bifurcation ◽  
Coexisting Attractors ◽  
One Dimensional ◽  
Poincaré Return Map ◽  
Smooth Dynamical System

In this work a one-dimensional piecewise-smooth dynamical system, representing a Poincaré return map for dynamical systems of the Lorenz type, is investigated. The system shows a bifurcation scenario similar to the classical period-doubling one, but which is influenced by so-called border collision phenomena and denoted as border collision period-doubling bifurcation scenario. This scenario is formed by a sequence of pairs of bifurcations, whereby each pair consists of a border collision bifurcation and a pitchfork bifurcation. The mechanism leading to this scenario and its characteristic properties, like symmetry-breaking and symmetry-recovering as well as emergence of coexisting attractors, are investigated.

Trajectories of intervals in one-dimensional dynamical systems

2007 ◽  
Vol 13 (8-9) ◽  
pp. 821-828 ◽  
Author(s):  
V. V. Fedorenko ◽  
E. Yu. Romanenko ◽  
A. N. Sharkovsky
Keyword(s):  
Dynamical Systems ◽  
One Dimensional
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