Non-i.i.d. random holomorphic dynamical systems and the generic dichotomy. (7th April 2022)

• Record Type: Journal Article
• Authors: Sumi, Hiroki; Watanabe, Takayuki
• Is Part Of: Nonlinearity. Volume 35:Number 4(2022)
• Page Start: 1857
• Page End: 1875
• Publication Date: 2022-04-07
• Subjects: random holomorphic dynamical systems -- Markov random dynamical systems -- noise-induced phenomenon -- randomness-induced phenomenon -- mean stable; 37F10 -- 37H10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac4a89
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider non-i.i.d. random holomorphic dynamical systems whose choice of maps depends on Markovian rules. We show that generically, such a system is mean stable or chaotic with full Julia set. If a system is mean stable, then the Lyapunov exponent is uniformly negative for every initial value and almost every random orbit. Moreover, we consider families of random holomorphic dynamical systems and show that the set of mean stable systems has full measure under certain conditions. The latter is a new result even for i.i.d. random dynamical systems.