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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We use the Smaller Alignment Index (SALI) to distinguish rapidly and withcertainty between ordered and chaotic motion in Hamiltonian flows. Thisdistinction is based on the different behavior of the SALI for the two cases:the index fluctuates around non--zero values for ordered orbits, while it tendsrapidly to zero for chaotic orbits. We present a detailed study of SALI'sbehavior for chaotic orbits and show that in this case the SALI exponentiallyconverges to zero, following a time rate depending on the difference of the twolargest Lyapunov exponents $\sigma_1$, $\sigma_2$ i.e. $SALI \proptoe^{-(\sigma_1-\sigma_2)t}$. Exploiting the advantages of the SALI method, wedemonstrate how one can rapidly identify even tiny regions of order or chaos inthe phase space of Hamiltonian systems of 2 and 3 degrees of freedom.Comment: 18 pages, 10 figures, accepted for publication in J. Phys.

Detecting order and chaos in Hamiltonian systems by the SALI method