Palindromic complexity of infinite words associated with simple Parry numbers

A simple Parry number is a real number beta > 1 such that the Renyi expansion of 1 is finite, of the form d(beta)(1) = t(1)...t(m). We study the palindromic structure of infinite aperiodic words mu(beta) that are the fixed point of a substitution associated with a simple Parry number beta. It is shown that the word mu(beta) contains infinitely many palindromes if and only if t(1) = t(2) =...= t(m-1) >= t(m). Numbers beta satisfying this condition are the so-called confluent Pisot numbers. If t(m) = 1 then mu(beta) is an Arnoux-Rauzy word. We show that if beta is a confluent Pisot number then P(n + 1) + P(n) = C(n + 1) - C(n) + 2, where P(n) is the number of palindromes and C(n) is the number of factors of length n in mu beta. We then give a complete description of the set of palindromes, its structure and properties.