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

R. Festa·A. Mazzino·D. Vincenzi
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Abstract

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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R. Festa, A. Mazzino, D. Vincenzi. 2000-12-06. At the very origin of chaos in three-dimensional dynamical systems. https://arxiv.org/abs/nlin/0012009

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