English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove that transport in the phase space of the "most strongly chaotic"dynamical systems has three different stages. Consider a finite Markovpartition (coarse graining) $\xi$ of the phase space of such a system. In thefirst short times interval there is a hierarchy with respect to the values ofthe first passage probabilities for the elements of $\xi$ and therefore finitetime predictions can be made about which element of the Markov partitiontrajectories will be most likely to hit first at a given moment. In the thirdlong times interval, which goes to infinity, there is an opposite hierarchy ofthe first passage probabilities for the elements of $\xi$ and therefore againfinite time predictions can be made. In the second intermediate times intervalthere is no hierarchy in the set of all elements of the Markov partition. Wealso obtain estimates on the length of the short times interval and show thatits length is growing with refinement of the Markov partition which shows thatpractically only this interval should be taken into account in many cases.These results demonstrate that finite time predictions for the evolution ofstrongly chaotic dynamical systems are possible. In particular, one can predictthat an orbit is more likely to first enter one subset of phase space thananother at a given moment in time. Moreover, these results suggest an algorithmwhich accelerates the process of escape through "holes" in the phase space ofdynamical systems with strongly chaotic behavior.

Where and When Orbits of Strongly Chaotic Systems Prefer to Go