MGAT10 - Chaos in rotating systems |
|
Speaker |
LEFRANC, Marc |
|
Talk Title |
Characterizing chaos with orientation-preserving dynamical triangulations |
|
Abstract |
The determinism principle, which states that dynamical state completely determines future time evolution, is a keystone of nonlinear dynamics and chaos theory. Since it precludes that two state space trajectories intersect, it is a core ingredient of a topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits embedded in a strange attractor. However, knot theory can be applied only to three-dimensional systems. Still, determinism applies in any dimension. We will describe an alternative framework in which this principle is enforced by constructing an orientation-preserving dynamics on triangulated surfaces and find that in three dimensions our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map. |
|
Talk view |
|
|
|
|