Sumsets and fixed points of substitutions

Balances for fixed points of primitive substitutions

An in!nite word de!ned over a !nite alphabet A is balanced if for any pair (!;!′) of factors of the same length and for any letter a in the alphabet ‖!|a − |!|a|6 1; where |!|a denotes the number of occurrences of the letter a in the word !. In this paper, we generalize this notion and introduce a measure of balance for an in!nite sequence. In the case of !xed points of primitive substitutions,...

2 00 7 Return Words in Fixed Points of Substitutions

We present three simple ideas which enable to determine easily the number of return words in some infinite words. Using these ideas, we give a new and very short proof of the fact that each factor of an Arnoux-Rauzy word of order m has exactly m return words. We describe the structure of return words for the Thue-Morse sequence and focus on infinite words which are associated to simple Parry nu...

Diagonal arguments and fixed points

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...

Coupled fixed points of generalized Kanann contraction and its applications

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...

Approximating fixed points of generalized nonexpansive mappings