Title: Tropical recurrent sequences,
Abstract: Tropical recurrent sequences are introduced satisfying a given vector (being
a tropical counterpart of classical linear recurrent sequences). We consider
the case when Newton polygon of the vector has a single (bounded) edge. In this
case there are periodic tropical recurrent sequences which are similar to
classical linear recurrent sequences. A question is studied when there exists a
non-periodic tropical recurrent sequence satisfying a given vector, and partial
answers are provided to this question. Also an algorithm is designed which
tests existence of non-periodic tropical recurrent sequences satisfying a given
vector with integer coordinates. Finally, we introduce a tropical entropy of a
vector and provide some bounds on it.