Higher dimensional shrinking target problem in beta dynamical systems

2019/08/06 by Hussain, Mumtaz, Wang, Weiliang
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1908.02098

Abstract

We consider the two dimensional shrinking target problem in the beta dynamical system for general β>1 and with the general error of approximations. Let f, g be two positive continuous functions. For any x₀,y₀∈[0,1], define the shrinking target set E(T_β, f,g):=\(x,y)∈ [0,1]²: \beginarrayll |T_βⁿx-x₀|

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