Existence of invariant idempotent measures by contractivity of idempotent Markov operators

TL;DR

This paper demonstrates that contractive idempotent Markov operators from max-plus normalized IFSs guarantee the existence of invariant measures, providing new proofs for their existence.

Contribution

It establishes the contractivity of idempotent Markov operators in max-plus IFSs and offers alternative proofs for invariant measure existence.

Findings

Idempotent Markov operators are contractive under natural metrics.

Existence of invariant idempotent measures is confirmed for such systems.

Provides new proof techniques for invariant measure existence.

Abstract

We prove that the idempotent Markov operator generated by contractive max plus normalized iterated function system (IFS) is also a contractive map w.r.t. natural metrics on the space of idempotent measures. This gives alternative proofs of the existence of invariant idempotent measures for such IFSs.