Fibonacci-like sequences and shift spaces in symbolic dynamics

2007/08/31 by Tonelli, R.
#05-(C38 #11B-(37 #37B-(10 #39 #40 #50) #62-(P35 #A15) #D05) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.0708.4370

Abstract

We afford the problem of counting the blocks of a given length made with symbols drawn from an alphabet and relate this number to Fibonacci-like recurrent relations. The recurrence polynomia allows to calculate the limit ratio of two adjacent terms and this information is used to determine the topological entropy of a discrete numbers of associate shift spaces. We then describe a scheme to build a shift space with a pre-selected entropy.

Related

• Entropy for symbolic dynamics with overlapping alphabets
• On d-approachability, entropy density and \mathscrB-free shifts
• Improvement Ergodic Theory For The Infinite Word \mathfrakF=\mathfrakF_b:=( _b f_n)_{n \geqslant 0} on Fibonacci Density
• Topological Dynamics indexed by words
• The natural measure of a symbolic dynamical system