Consider a monic polynomial with integer coefficients: , .

The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.

Consider a square matrix with positive integer entries. By Perron-Frobenius Theorem, there is a unique positive eigenvalue . Moreover, it admits an eigenvector of all positive entries, and satisfies for any other eigenvalue of . In particular, for any of its Galois conjugates. Such a number is called a Perron number. More generally, a weak Perron number is a real algebraic integer whose modulus is greater than or equal to that of all of its Galois conjugates.

Let be a continuous map on the interval , and the topological entropy. Assume is postcritically finite: is a finite set. Then the partition of along the postcritical set is a Markov partition for , since (1) the endpoints are sent to endpoints, (2) every folding corresponds to a critical point of . Therefore, is the leading eigenvalue of the incidence matrix associated to the Markov partition . It follows that is a weak Perron number.