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1
Content available remote On the C⁰-closing lemma
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nr 2
131-138
EN
A proof of the C⁰-closing lemma for noninvertible discrete dynamical systems and its extension to the noncompact case are presented.
2
Content available remote A note on ω-limit set of a tree map
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EN
Let T be a tree and f : T →T be continuous. Denote by P(f) and ω(x, f) the set of periodic points of f and w-limit set of x under f respectively. Write ᴧ(f) = UxϵTω(x,f). In this paper, we show that if ...[wzór], then ω(x, f) is an infinite minimal set.
3
Content available remote All solenoids of piecewise smooth maps are period doubling
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EN
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.
4
75%
EN
We give necessary and sufficient conditions for the existence of some general solutions of the following two functional inequalities with an unknown real function phi: phi(Fx) is less than or equal to eta(phi(x)) and gamma(phi(Fx)) is less than or equal to phi(x). As an application we establish reciprocals to fixed point theorems of Matkowski and Wong. This extends an earlier result of Bessaga on a converse to the Banach contraction principle.
5
Content available remote On common fixed points of commuting triangular maps
63%
EN
We give some conditions under which commuting triangular maps have a common fixed point. Some of them provide analogons of known results for maps of a real interval.
6
Content available remote On linear chaos in function spaces
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EN
We show that, in Lp(0,∞) ( 1≤p<∞ ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C0[0,∞) and describe the spectra of the weighted translations provided the underlying spaces are complex.
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