Displaying similar documents to “Inverse limits of certain interval mappings as attractors in two dimensions”

Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms

Sarah Holte (1995)

Colloquium Mathematicae


In this paper we address the following question due to Marcy Barge: For what f:I → I is it the case that the inverse limit of I with single bonding map f can be embedded in the plane so that the shift homeomorphism f ^ extends to a diffeomorphism ([BB, Problem 1.5], [BK, Problem 3])? This question could also be phrased as follows: Given a map f:I → I, find a diffeomorphism F : 2 2 so that F restricted to its full attracting set, k 0 F k ( 2 ) , is topologically conjugate to f ^ : ( I , f ) ( I , f ) . In this situation, we say that...