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arXiv · 2008.09792

On the pointwise Lyapunov exponent of holomorphic maps

Israel Or Weinstein
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Abstract

We prove that for any holomorphic map, and any bounded orbit which does not accumulate to a singular set or to an attracting cycle, its lower Lyapunov exponent is non-negative. The same result holds for unbounded orbits, for maps with a bounded singular set. Furthermore, the orbit may accumulate to infinity or to a singular set, as long as it is slow enough.

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Israel Or Weinstein. 2020-08-22. On the pointwise Lyapunov exponent of holomorphic maps. https://doi.org/10.4064/fm847-1-2020

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