On families of invariant lines of a Brouwer homeomorphism

ABSTRACT

We present properties of equivalence classes of the codivergency relation defined for a Brouwer homeomorphism for which there exists a family of invariant pairwise disjoint lines covering the plane. In particular, using the codivergency relation we describe the sets of regular and irregular points for such Brouwer homeomorphisms. Moreover, we show that under this assumption the interior of each equivalence class of this relation is invariant and simply connected.

KEYWORDS:

• Brouwer homeomorphism
• discrete dynamical system
• codivergency relation
• regular point
• invariant line

2000 MaTHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 39B12
• Secondary 54H20
• 37E30

Disclosure statement

No potential conflict of interest was reported by the author.