The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity

Details The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity

2007-05-10

arxiv.org/abs/0705.1459v3

PhysA Vol 387/8-9 pp 1907-1925

Nonlinear Sciences

Chaotic Dynamics

19 pages, 12 figures, accepted for publication by Physica A

Scientific paper

10.1016/j.physa.2007.11.024

We study the connection between the appearance of a `metastable' behavior of weakly chaotic orbits, characterized by a constant rate of increase of the Tsallis q-entropy (Tsallis 1988), and the solutions of the variational equations of motion for the same orbits. We demonstrate that the variational equations yield transient solutions, lasting for long time intervals, during which the length of deviation vectors of nearby orbits grows in time almost as a power-law. The associated power exponent can be simply related to the entropic exponent for which the q-entropy exhibits a constant rate of increase. This analysis leads to the definition of a new sensitive indicator distinguishing regular from weakly chaotic orbits, that we call `Average Power Law Exponent' (APLE). We compare the APLE with other established indicators of the literature. In particular, we give examples of application of the APLE in a) a thin separatrix layer of the standard map, b) the stickiness region around an island of stability in the same map, and c) the web of resonances of a 4D symplectic map. In all these cases we identify weakly chaotic orbits exhibiting the `metastable' behavior associated with the Tsallis q-entropy.

Affiliated with

Also associated with

No associations

Rating

The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-600774