Resumen de Dold Coefficients of Quasi-unipotent Homeomorphisms of Orientable Surfaces

Grzegorz Graff , Waclaw Marzantowicz, Łukasz Patryk Michalak

• The sequence of Dold coefficients (an( f )) of a self-map f : X → X forms a dual sequence to the sequence of Lefschetz numbers (L( f n)) of iterations of f under the Möbius inversion formula. The set AP( f ) = {n : an( f ) = 0} is called the set of algebraic periods of f . Both the set of algebraic periods and sequence of Dold coefficients play an important role in dynamical systems and periodic point theory. In this work we provide a description of surface homeomorphisms with bounded (L( f n)) (quasi-unipotent maps) in terms of Dold coefficients. We also discuss the problem of minimization of the genus of a surface for which one can realize a given set of natural numbers as the set of algebraic periods. Finally, we compute and list all possible Dold coefficients and algebraic periods for a given orientable surface with small genus and give some geometrical applications of the obtained results.