Dynamics of "leaking" hamiltonian systems

Judit Schneider, T. Tél, Zoltán Neufeld

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

In order to understand the dynamics in more detail, in particular for visualizing the space-filling unstable foliation of closed chaotic Hamiltonian systems, we propose to leak them up. The cutting out of a finite region of their phase space, the leak, through which escape is possible, leads to transient chaotic behavior of nearly all the trajectories. The never-escaping points belong to a chaotic saddle whose fractal unstable manifold can easily be determined numerically. It is an approximant of the full Hamiltonian foliation, the better the smaller the leak is. The escape rate depends sensitively on the orientation of the leak even if its area is fixed. The applications for chaotic advection, for chemical reactions superimposed on hydrodynamical flows, and in other branches of physics are discussed.

Original languageEnglish
Article number066218
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume66
Issue number6
DOIs
Publication statusPublished - Dec 2002

Fingerprint

Foliation
Hamiltonian Systems
escape
Chaotic Advection
Escape Rate
Unstable Manifold
Transient Behavior
saddles
Saddle
Chaotic Behavior
advection
Chemical Reaction
Chaotic System
Fractal
Phase Space
fractals
chemical reactions
Branch
Unstable
Physics

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Dynamics of "leaking" hamiltonian systems. / Schneider, Judit; Tél, T.; Neufeld, Zoltán.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 66, No. 6, 066218, 12.2002.

Research output: Contribution to journalArticle

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