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Manifolds on the verge of a hyperbolicity breakdown
Haro, Àlex; Llave, Rafael de la
Universitat de Barcelona
We study numerically the disappearance of normally hyperbolic invariant tori in quasiperiodic systems and identify a scenario for their breakdown. In this scenario, the breakdown happens because two invariant directions of the transversal dynamics come close to each other, losing their regularity. On the other hand, the Lyapunov multipliers associated with the invariant directions remain more or less constant. We identify notable quantitative regularities in this scenario, namely that the minimum angle between the two invariant directions and the Lyapunov multipliers have power law dependence with the parameters. The exponents of the power laws seem to be universal.
Física estadística
Sistemes dinàmics diferenciables
Dinàmica de fluids
Statistical physics
Differentiable dynamical systems
Fluid dynamics
(c) American Institute of Physics, 2006
American Institute of Physics

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