On the pointwise Lyapunov exponent of holomorphic maps
Volume 252 / 2021
Fundamenta Mathematicae 252 (2021), 39-51
MSC: Primary 37F10, 37F15, 37F50.
DOI: 10.4064/fm847-1-2020
Published online: 23 July 2020
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.
