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Arcsine law for core random dynamics | | Fumihiko Nakamura
; Yushi Nakano
; Hisayoshi Toyokawa
; Kouji Yano
; | | Date: |
1 Jun 2022 | | 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. | | Source: | arXiv, 2206.00226 | | Services: | Forum | Review | PDF | Favorites | |
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