Generating sequences of Lefschetz numbers of iterates

Abstract

Du, Huang and Li showed in 2003 that the class of Dold-Fermat sequences coincides with the class of Newton sequences, which are defined in terms of socalled generating sequences. The sequences of Lefschetz numbers of iterates form an important subclass of Dold-Fermat (thus also Newton) sequences. In this paper we characterize generating sequences of Lefschetz numbers of iterates.

Periodic structure of the transversal maps on surfaces

“…The Lefschetz numbers of period m were introduced in [4], see also [13,1,11]; for more recent developments in the characterization of these numbers see [8].…”

Dold sequences, periodic points, and dynamics

“…Generating sequences of Lefschetz numbers were considered by Graff et al [52], and a certain characterisation of generating sequences of Lefschetz numbers of iterations was given. Here we will describe a simple computational criterion for verifying that a given sequence (c n ) is not a generating sequence of a Lefschetz sequence (provided the dimensions of respective matrices are bounded from above).…”

Dold sequences, periodic points, and dynamics

“…Generating sequences for Lefschetz sequences. Generating sequences of Lefschetz numbers were considered by Graff et al [40], and a certain characterization of generating sequences of Lefschetz numbers of iterations was given. Here we will describe a simple computational criterion for verifying that a given sequence (c n ) is not a generating sequence of a Lefschetz sequence (provided the dimensions of respective matrices are bounded from above).…”