Behavior of the dispersion of the stochastic Lyapunov function for the Feigenbaum map

In the theory of Feigenbaum’s universality the Feigenbaum’s and its unsteady separatrice passing through. The unsteady separatrice is the one-parameter family of unimodal maps of the interval [−1,1]. In the present paper we study the sequence xn+1 = g (xn,τn) + ξn+1,n ≥ 1 of small stochastic perturb...

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Bibliographic Details
Main Authors: Abdukhakimov, Saidakhmat, Pulatov, Bakhtiyor, Ibrohimov, Javohir
Format: Conference Proceeding
Language:English
Subjects:
Liapunov functions
Online Access:Get full text
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Summary:In the theory of Feigenbaum’s universality the Feigenbaum’s and its unsteady separatrice passing through. The unsteady separatrice is the one-parameter family of unimodal maps of the interval [−1,1]. In the present paper we study the sequence xn+1 = g (xn,τn) + ξn+1,n ≥ 1 of small stochastic perturbations of maps g(x,t) from unsteady separatrice Γ(u)(g), It is proved the theorem on behavior of variance of linear part of random value xn.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0241921