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arXiv · 1308.3734

Numerical estimate of infinite invariant densities: application to Pesin-type identity

Nickolay Korabel·Eli Barkai
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Abstract

Weakly chaotic maps with unstable fixed points are investigated in the regime where the invariant density is non-normalizable. We propose that the infinite invariant density of these maps can be estimated using as the long time limit of t^(1-alpha) rho(x, t), in agreement with earlier work of Thaler. Here rho(x, t) is the normalizable density of particles. This definition uniquely determines the infinite density and is a valuable tool for numerical estimations. We use this density to estimate the subexponential separation lambda_alpha of nearby trajectories. For a particular map introduced by Thaler we use an analytical expression for the infinite invariant density to calculate lambda_alpha exactly, which perfectly matches simulations without fitting. Misunderstanding which recently appeared in the literature is removed.

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Nickolay Korabel, Eli Barkai. 2013-08-16. Numerical estimate of infinite invariant densities: application to Pesin-type identity. https://doi.org/10.1088/1742-5468%2F2013%2F08%2Fp08010

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