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Tytuł artykułu

Period doubling, entropy, and renormalization

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We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point. Similar techniques then allow us to show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable with the diameters of all periodic intervals going to zero as the period goes to infinity.
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  • Department of Mathematics, Rutgers University, Newark, New Jersey 07102, U.S.A.
  • IBM, P.O. Box 218, Yorktown Heights, New York 10598, U.S.A.
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