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 test a Markov chain approximation to the segment description (Li, 2007) ofchaos (and turbulence) on a tent map, the Minea system, the H\'enon map, andthe Lorenz system. For the tent map, we compute the probability transitionmatrix of the Markov chain on the segments for segment time length (iterations)$T = 1, 2, 3, 100$. The matrix has $1, 2, 4$ tents corresponding to $T = 1, 2,3$; and is almost uniform for $T = 100$. As $T \ra +\infty$, our conjecture isthat the matrix will approach a uniform matrix (i.e. every entry is the same).For the simple fixed point attractor in the Minea system, the Reynolds averageperforms excellently and better than the maximal probability Markov chain andsegment linking. But for the strange attractors in the H\'enon map, and theLorenz system, the Reynolds average performs very poorly and worse than themaximal probability Markov chain and segment linking.

A Markov Chain Approximation of a Segment Description of Chaos