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All solenoids of piecewise smooth maps are period doubling

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Alsedà L., López V. J., L'ubomír Snoha

Fundamenta Mathematicae

1998

tom 157

nr 2-3

121-138

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 $p_1 < ... < p_n$ is a periodic orbit of a continuous map f then there is a union set ${q_1,..., q_{n-1}}$ of some periodic orbits of f such that $p_i < q_i < p_{i+1}$ for any i.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Alsedà L.

1 L'ubomír Snoha

1 López V. J.

1 1998

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All solenoids of piecewise smooth maps are period doubling