Time-metric equivalence and dimension change under time reparameterizations

Details Time-metric equivalence and dimension change under time reparameterizations Time-metric equivalence and dimension change under time reparameterizations

2009-05-20

arxiv.org/abs/0905.3416v1

Phys.Rev.E79:065202,2009

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevE.79.065202

We study the behavior of dynamical systems under time reparameterizations, which is important not only to characterize chaos in relativistic systems but also to probe the invariance of dynamical quantities. We first show that time transformations are locally equivalent to metric transformations, a result that leads to a transformation rule for all Lyapunov exponents on arbitrary Riemannian phase spaces. We then show that time transformations preserve the spectrum of generalized dimensions D_q except for the information dimension D_1, which, interestingly, transforms in a nontrivial way despite previous assertions of invariance. The discontinuous behavior at q=1 can be used to constrain and extend the formulation of the Kaplan-Yorke conjecture.

Affiliated with

Also associated with

No associations

Rating

Time-metric equivalence and dimension change under time reparameterizations 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 Time-metric equivalence and dimension change under time reparameterizations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Time-metric equivalence and dimension change under time reparameterizations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-444510