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arXiv · 2206.00226

Arcsine law for random dynamics with a core

Fumihiko Nakamura·Yushi Nakano·Hisayoshi Toyokawa·Kouji Yano
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Abstract

In their recent paper [8], G.Hata and the fourth author first gave an example of random iterations of two piecewise linear interval maps without (deterministic) indifferent periodic points for which the arcsine law -- a characterization of intermittent dynamics in infinite ergodic theory -- holds. The key in the proof of the result is the existence of a Markov partition preserved by each interval maps. In the present paper, we give a class of random iterations of two interval maps without indifferent periodic points but satisfying the arcsine law, by introducing a concept of core random dynamics. As applications, we show that the generalized arcsine law holds for generalized Hata-Yano maps and piecewise linear versions of Gharaei-Homburg maps, both of which do not have a Markov partition in general.

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Fumihiko Nakamura, Yushi Nakano, Hisayoshi Toyokawa, Kouji Yano. 2022-06-01. Arcsine law for random dynamics with a core. https://doi.org/10.1088/1361-6544%2Facb398

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