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Interval projections of self-similar sets

Published online by Cambridge University Press:  14 June 2018

ÁBEL FARKAS
ÁBEL FARKAS*
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 9190401, Israel email [email protected]
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Abstract

We show if $K$ is a self-similar $1$-set that either satisfies the strong separation condition or is defined via homotheties then there are at most finitely many lines through the origin such that the projection of $K$ onto them is an interval.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 1 , January 2020 , pp. 194 - 212
Copyright
© Cambridge University Press, 2018 

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