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A class of tridiagonal operators associated to some subshifts

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Hernández-Becerra C., Itzá-Ortiz B. A.

Open Mathematics

2016

tom 14

nr 1

352-360

We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N. Chandler-Wilde et al. and R. Hagger, which rely on limit operator techniques, we are able to provide more general results although the closure of the numerical range needs to be taken.

Chaotic behaviour of the map x ↦ ω(x, f)

100%

D’Aniello E., Steele T.

Open Mathematics

2014

tom 12

nr 4

584-592

Let K(2ℕ) be the class of compact subsets of the Cantor space 2ℕ, furnished with the Hausdorff metric. Let f ∈ C(2ℕ). We study the map ω f: 2ℕ → K(2ℕ) defined as ω f (x) = ω(x, f), the ω-limit set of x under f. Unlike the case of n-dimensional manifolds, n ≥ 1, we show that ω f is continuous for the generic self-map f of the Cantor space, even though the set of functions for which ω f is everywhere discontinuous on a subsystem is dense in C(2ℕ). The relationships between the continuity of ω f and some forms of chaos are investigated.

Ograniczanie wyników

2 Open Mathematics

1 D’Aniello E.

1 Hernández-Becerra C.

1 Itzá-Ortiz B. A.

1 Steele T.

1 2016

1 2014

Wyniki wyszukiwania

A class of tridiagonal operators associated to some subshifts

Chaotic behaviour of the map x ↦ ω(x, f)