Continuous symmetry reduction and return maps for high-dimensional flows

Details Continuous symmetry reduction and return maps for high-dimensional flows Continuous symmetry reduction and return maps for high-dimensional flows

2010-06-11

arxiv.org/abs/1006.2362v1

Physica D 240 (2011) 187-198

Nonlinear Sciences

Chaotic Dynamics

32 pages, 7 figures

Scientific paper

10.1016/j.physd.2010.07.010

We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of moving frames (or method of slices) the state space is sliced locally in such a way that each group orbit of symmetry-equivalent points is represented by a single point. In either approach, numerical computations can be performed in the original state-space representation, and the solutions are then projected onto the symmetry-reduced state space. The two methods are illustrated by reduction of the complex Lorenz system, a 5-dimensional dissipative flow with rotational symmetry. While the Hilbert polynomial basis approach appears unfeasible for high-dimensional flows, symmetry reduction by the method of moving frames offers hope.

Affiliated with

Also associated with

No associations

Rating

Continuous symmetry reduction and return maps for high-dimensional flows 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 Continuous symmetry reduction and return maps for high-dimensional flows, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuous symmetry reduction and return maps for high-dimensional flows will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-78024