Decompositions Of Sturmian Words

In recent yeas, combinatorial properties of finite and infinite words have become significantly important in the fields of physics, biology, mathematics and computer science. In particular, the fascinating family of Sturmian words has been the subject of many papers. These words, which represent the simplest family of quasicrystals, have numerous applications in various fields of mathematics , such as symbolic dynamics, the study of continued fraction expansion ,and also in some domains of physics and computer science. So it is very important for the study of Sturmian words.Sturmian words are aperiodic infinite words with exactly n+1distinct factors of length n ,for each n. The thesis is organized as follows:In the first part in the thesis we introduce the definitions and properties of Fibonacci words,singular words,Lyndon words,characteristics Sturmian words,standard words and the adjoining words of singular words.In the second part, we give the result of the decomposition. At first we give a decomposition of Fibonacci words into singular words and Lydon words, then we give a decomposition of characteristics Sturmian words into generalized adjoining singular words, we give the results about the adjoining words of singular words.