All solenoids of piecewise smooth maps are period doubling
Alsedà, Lluís ; Jiménez López, Víctor ; Snoha, L’ubomír
Fundamenta Mathematicae, Tome 158 (1998), p. 121-138 / Harvested from The Polish Digital Mathematics Library
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We show that piecewise smooth maps with a finite number of pieces of monotonicity and nowhere vanishing Lipschitz continuous derivative can have only period doubling solenoids. The proof is based on the fact that if p1<...<pn is a periodic orbit of a continuous map f then there is a union set q1,...,qn-1 of some periodic orbits of f such that pi<qi<pi+1 for any i.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:212281 
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     title = {All solenoids of piecewise smooth maps are period doubling},
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     year = {1998},
     pages = {121-138},
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Alsedà, Lluís; Jiménez López, Víctor; Snoha, L’ubomír. All solenoids of piecewise smooth maps are period doubling. Fundamenta Mathematicae, Tome 158 (1998) pp. 121-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p121bwm/

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