At the very origin of chaos in three-dimensional dynamical systems

Details At the very origin of chaos in three-dimensional dynamical systems At the very origin of chaos in three-dimensional dynamical systems

2000-12-06

arxiv.org/abs/nlin/0012009v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 figures

Scientific paper

The mechanism responsible for the emergence of chaotic behavior has been identified analytically within a class of three-dimensional dynamical systems which generalize the well-known E.N. Lorenz 1963 system. The dynamics in the phase space has been reformulated in terms of a first-exit-time problem. Chaos emerges due to discontinuous solutions of a transcendental problem ruling the time for a particle to cross a potential wall. Numerical results point toward the genericity of the new found mechanism.

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