Uncertainty Relation for Chaos

Details Uncertainty Relation for Chaos Uncertainty Relation for Chaos

2011-12-09

arxiv.org/abs/1112.2101v1

Physics

Mathematical Physics

5 pages, 6 figures

Scientific paper

A necessary condition for the emergence of chaos is given. It is well known that the emergence of chaos requires a positive exponent which entails diverging trajectories. Here we show that this is not enough. An additional necessary condition for the emergence of chaos in the region where the trajectory of the system goes through, is that the product of the maximal positive exponent times the duration in which the system configuration point stays in the unstable region should exceed unity. We give a theoretical analysis justifying this result and a few examples.

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