Computing the measure of nonattracting chaotic sets
Physica D Nonlinear PhenomenaPublished 1 September 1997
Joeri Jacobs, Edward Ott, Celso Grebogi
Citations12
SJR quartileQ1
SJR score0.94
SNIP1.39
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
Recently, a numerical method, called the PIM-triple algorithm, has been formulated for generating long orbits on nonattracting chaotic sets. We investigate under which conditions the measure for a nonattracting invariant set generated by the PIM-triple algorithm agrees with the natural measure.
Keywords
MathematicsPhysics and Astronomy
Physics Today<i>An Introduction to Chaotic Dynamical Systems</i>
2,373 Citations1987Robert L. Devaney, Jean‐Pierre Eckmann
Physica D Nonlinear PhenomenaCrises, sudden changes in chaotic attractors, and transient chaos
1,317 Citations1983Celso Grebogi, Edward Ott +1 more
Physica D Nonlinear PhenomenaFractal basin boundaries
598 Citations1985Steven W. McDonald, Celso Grebogi +2 more
Physical Review LettersCommunicating with chaos
569 Citations1993Scott Hayes, Celso Grebogi +1 more
It is shown that the recent realization that chaos can be controlled with small perturbations can be utilized to cause the symbolic dynamics of a chaotic system to track a prescribed symbol sequence, thus allowing us to encode any desired message in the wave form from a chaotic oscillator.
Physica D Nonlinear PhenomenaRepellers, semi-attractors, and long-lived chaotic transients
315 Citations1985Hölger Kantz, Peter Grassberger
Physical Review LettersCritical Exponent of Chaotic Transients in Nonlinear Dynamical Systems
285 Citations1986Celso Grebogi, Edward Ott +1 more
A theory determining $\ensuremath{\gamma}$ for two-dimensional maps is developed and compared with numerical experiments to determine the critical exponent of the chaotic transient.
Directions in chaos
225 Citations1987Bai-Lin Hao
Chaos An Interdisciplinary Journal of Nonlinear ScienceChaotic scattering: An introduction
185 Citations1993Edward Ott, Tamás Tél
This issue of Chaos provides an up-to-date survey of the range of work in this important field of study, with new analytical techniques being developed and with experiments being carried out.
Physica D Nonlinear PhenomenaA procedure for finding numerical trajectories on chaotic saddles
175 Citations1989Helena E. Nusse, James A. Yorke
Journal of the Optical Society of America BGlobal dynamical behavior of the optical field in a ring cavity
160 Citations1985Stephen Hammel, Jerome V. Moloney +1 more
Physics Letters AStrange saddles and the dimensions of their invariant manifolds
139 Citations1988Guan-Hsong Hsu, Edward Ott +1 more
NonlinearityHow often are chaotic saddles nonhyperbolic?
111 Citations1993Y -C Lai, Celso Grebogi +2 more
Ergodic Theory and Dynamical SystemsAnalysis of a procedure for finding numerical trajectories close to chaotic saddle hyperbolic sets
30 Citations1991Helena E. Nusse, James A. Yorke
