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The disjoint arcs property for homogeneous curves

100%

Krupski P.

Fundamenta Mathematicae

1994-1995

tom 146

nr 2

159-169

The local structure of homogeneous continua (curves) is studied. Components of open subsets of each homogeneous curve which is not a solenoid have the disjoint arcs property. If the curve is aposyndetic, then the components are nonplanar. A new characterization of solenoids is formulated: a continuum is a solenoid if and only if it is homogeneous, contains no terminal nontrivial subcontinua and small subcontinua are not ∞-ods.

All solenoids of piecewise smooth maps are period doubling

100%

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.

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2 Fundamenta Mathematicae

1 Alsedà L.

1 Krupski P.

1 L'ubomír Snoha

1 López V. J.

1 1998

1 1995

Wyniki wyszukiwania

The disjoint arcs property for homogeneous curves

All solenoids of piecewise smooth maps are period doubling