Collision and symmetry-breaking in the transition to strange nonchaotic attractors

Details Collision and symmetry-breaking in the transition to strange nonchaotic attractors Collision and symmetry-breaking in the transition to strange nonchaotic attractors

1999-09-30

arxiv.org/abs/chao-dyn/9909039v1

Phys.Rev.Lett.83:4530,1999

Nonlinear Sciences

Chaotic Dynamics

To be appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.83.4530

Strange nonchaotic attractors (SNAs) can be created due to the collision of an invariant curve with itself. This novel ``homoclinic'' transition to SNAs occurs in quasiperiodically driven maps which derive from the discrete Schr\"odinger equation for a particle in a quasiperiodic potential. In the classical dynamics, there is a transition from torus attractors to SNAs, which, in the quantum system is manifest as the localization transition. This equivalence provides new insights into a variety of properties of SNAs, including its fractal measure. Further, there is a {\it symmetry breaking} associated with the creation of SNAs which rigorously shows that the Lyapunov exponent is nonpositive. By considering other related driven iterative mappings, we show that these characteristics associated with the the appearance of SNA are robust and occur in a large class of systems.

Affiliated with

Also associated with

No associations

Rating

Collision and symmetry-breaking in the transition to strange nonchaotic attractors 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 Collision and symmetry-breaking in the transition to strange nonchaotic attractors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Collision and symmetry-breaking in the transition to strange nonchaotic attractors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-570449