Statistical and Deterministic Dynamics of Maps with Memory

2016/04/24 by Góra, Paweł, Boyarsky, Abraham, Li, Zhenyang +1
#37A05 #37A10 #37E05 #37E30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.06991

Abstract

We consider a dynamical system to have memory if it remembers the current state as well as the state before that. The dynamics is defined as follows: x_n+1=T_α(x_n-1,x_n)=τ(α⋅ x_n+(1-α)⋅ x_n-1), where τ is a one-dimensional map on I=[0,1] and 0

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