A 2-equivalent Kelley continuum

Islas, Carlos

doi:10.3336/gm.46.1.18

Cited by 2 publications

(3 citation statements)

References 9 publications

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“…We are also grateful to Gerardo Acosta for bringing the Islas work [16] to our attention and to the anonymous referee for bringing to our attention the problem whether constructed continua are Suslinean or not. We are also grateful to Gerardo Acosta for bringing the Islas work [16] to our attention and to the anonymous referee for bringing to our attention the problem whether constructed continua are Suslinean or not.…”

Section: Acknowledgementsmentioning

confidence: 99%

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On indecomposability in chaotic attractors

Boroński¹,

Oprocha

2015

Proc. Amer. Math. Soc.

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We exhibit a Li-Yorke chaotic interval map F such that the inverse limit X F = lim ← − {F, [0, 1]} does not contain an indecomposable subcontinuum. Our result contrasts with the known property of interval maps: if ϕ has positive entropy then X ϕ contains an indecomposable subcontinuum. Each subcontinuum of X F is homeomorphic to one of the following: an arc, or X F , or a topological ray limiting to X F . Through our research, we found that it follows that X F is a chaotic attractor of a planar homeomorphism. In addition, F can be modified to give a cofrontier that is a chaotic attractor of a planar homeomorphism but contains no indecomposable subcontinuum. Finally, F can be modified, without removing or introducing new periods, to give a chaotic zero entropy interval map, such that the corresponding inverse limit contains the pseudoarc.

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Section: Acknowledgementsmentioning

confidence: 99%

“…It is worth emphasizing, that an interesting example of 2-equivalent continuum was recently constructed by Islas [16], who proved that his example was hereditarily decomposable but without investigating the dynamical properties of it. As we exhibited in the above proof, X f is 3-equivalent.…”

Section: Lemmamentioning

confidence: 99%

On indecomposability in chaotic attractors

Boroński¹,

Oprocha

2015

Proc. Amer. Math. Soc.

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“…We mention that such operators are called fundamental reducible, see e.g. [47], and that they possess a well-developed spectral and perturbation theory, cf [36,40,43,[47][48][49][50][51][52].…”

Section: Lemmamentioning

confidence: 99%

On domains of {\cal P}{\cal T} symmetric operators related to −y″(x) + (− 1)ⁿx²ⁿy(x)

Azizov¹,

Trunk²

2010

J. Phys. A: Math. Theor.

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In the recent years a generalization of Hermiticity was investigated using a complex deformation H = p 2 + x 2 (ix) ǫ of the harmonic oscillator Hamiltonian, where ǫ is a real parameter. These complex Hamiltonians, possessing PT symmetry (the product of parity and time reversal), can have real spectrum. We will consider the most simple case: ǫ even. In this paper we describe all self-adjoint (Hermitian) and at the same time PT symmetric operators associated to H = p 2 + x 2 (ix) ǫ . Surprisingly it turns out that there are a large class of self-adjoint operators associated to H = p 2 + x 2 (ix) ǫ which are not PT symmetric.

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A 2-equivalent Kelley continuum

Cited by 2 publications

References 9 publications

On indecomposability in chaotic attractors

On indecomposability in chaotic attractors

On domains of {\cal P}{\cal T} symmetric operators related to −y″(x) + (− 1)ⁿx²ⁿy(x)

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A 2-equivalent Kelley continuum

Cited by 2 publications

References 9 publications

On indecomposability in chaotic attractors

On indecomposability in chaotic attractors

On domains of {\cal P}{\cal T} symmetric operators related to −y″(x) + (− 1)nx2ny(x)

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On domains of {\cal P}{\cal T} symmetric operators related to −y″(x) + (− 1)ⁿx²ⁿy(x)