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arXiv · 2502.18628

Uniform positivity of the Lyapunov exponent for $C^1$ monotone potentials generated by the cat map

Nicholas Chiem
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Abstract

We consider an Arnold's Cat Map generated $C^1$ bounded potential with the directional derivative in the unstable direction bounded away from zero. We show that the Lyapunov exponent for the associated Shr\"odinger Operator is uniformly positive for all energies provided the coupling is sufficiently large.

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Nicholas Chiem. 2025-02-25. Uniform positivity of the Lyapunov exponent for $C^1$ monotone potentials generated by the cat map. https://arxiv.org/abs/2502.18628

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