Prime end rotation numbers of invariant separating contunua of annular homeomorphisms

Publication date: 5 December 2010

Abstract: Let

f

be a homeomorphism of the closed annulus

A

isotopic to the identity, and let

X s u b s e t m I n t A

be an

f

-invariant continuum which separates

A

into two domains, the upper domain

U_{+}

and the lower domain

U_{-}

. Fixing a lift of

f

to the universal cover of

A

, one defines the rotation set

i l d e h o (X)

of

X

by means of the invariant probabilities on

X

, as well as the prime end rotation number

c h e c k h o_{p} m

of

U_{p} m

. The purpose of this paper is to show that

c h e c k h o_{p} m

belongs to

i l d e h o (X)

for any separating invariant continuum

X

.

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