Estimating generating partitions of chaotic systems by unstable periodic orbits

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 2, 2000, Pages 1353-1356

  Davidchack, Ruslan L ^a   Lai, Ying Cheng ^b   Bollt, Erik M ^c   Dhamala, Mukeshwar ^a  

^a UNIVERSITY OF KANSAS   (United States)

^b Arizona State University   (United States)

^c UNITED STATES NAVAL ACADEMY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC DYNAMICS; INFINITE NUMBERS; INVARIANT SET; PERIODIC ORBITS; PROXIMITY FUNCTIONS; SYMBOLIC DYNAMICS; TASK-BASED; UNSTABLE PERIODIC ORBITS;

CHAOTIC SYSTEMS;

EID: 0001167045     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.1353     Document Type: Article

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26. We find that initial assignment of symbols to periodic orbits of the lowest period does not affect the final generating partition. As the period increases, the size of the phase-space region that contains the generating partition decreases rapidly.
27. Loosely, the UPO’s arrange themselves in regions of higher natural measure, which is related to the Sinai-Bowen-Ruelle (SBR) measure, or the measure along unstable manifolds (the darker colored regions in the picture). The voids, or white regions which “stripe” the attractor, reveal shadows of the stable manifold. A partition curve arises automatically where the white stripes and the colored stripes seem to be tangent.