Article
Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase Space Public Deposited
https://scholar.colorado.edu/concern/articles/hq37vp21f
- Abstract
- The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For area-preserving maps, this has been attributed to the stickiness of boundary circles, which separate chaotic and regular components. Though such dynamics has been extensively studied, a full understanding depends on many fine details that typically are beyond experimental and numerical resolution. This calls for a statistical approach, the subject of the present work. We calculate the statistics of the boundary circle winding numbers, contrasting the distribution of the elements of their continued fractions to that for uniformly selected irrationals. Since phase space transport is of great interest for dynamics, we compute the distributions of fluxes through island chains. Analytical fits show that the “level” and “class” distributions are distinct, and evidence for their universality is given.
- Creator
- Date Issued
- 2014-12-31
- Academic Affiliation
- Journal Title
- Journal Volume
- 90
- File Extent
- 062923
- Last Modified
- 2019-12-05
- Resource Type
- Rights Statement
- DOI
- 10.1103/PhysRevE.90.062923
- Language
Relationships
Items
Thumbnail | Title | Date Uploaded | Visibility | Actions |
---|---|---|---|---|
statisticsOfTheIslandAroundIslandHierarchyInHamiltonianP.pdf | 2019-12-05 | Public | Download |