Statistics of the island-around-island hierarchy in Hamiltonian phase space

Or Alus, Shmuel Fishman, and James D. Meiss
Phys. Rev. E 90, 062923 – Published 31 December 2014

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
6 More
  • Received 7 November 2014

DOI:https://doi.org/10.1103/PhysRevE.90.062923

©2014 American Physical Society

Authors & Affiliations

Or Alus* and Shmuel Fishman

  • Physics Department, Technion–Israel Institute of Technology, Haifa 3200, Israel

James D. Meiss

  • Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA

  • *oralus@tx.technion.ac.il
  • fishman@physics.technion.ac.il
  • james.meiss@colorado.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 90, Iss. 6 — December 2014

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×