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Denseness and Borel complexity of some sets of vector measures

Zbigniew Lipecki (2004)

Studia Mathematica

Let ν be a positive measure on a σ-algebra Σ of subsets of some set and let X be a Banach space. Denote by ca(Σ,X) the Banach space of X-valued measures on Σ, equipped with the uniform norm, and by ca(Σ,ν,X) its closed subspace consisting of those measures which vanish at every ν-null set. We are concerned with the subsets ν ( X ) and ν ( X ) of ca(Σ,X) defined by the conditions |φ| = ν and |φ| ≥ ν, respectively, where |φ| stands for the variation of φ ∈ ca(Σ,X). We establish necessary and sufficient conditions...

Descriptive compact spaces and renorming

L. Oncina, M. Raja (2004)

Studia Mathematica

We study the class of descriptive compact spaces, the Banach spaces generated by descriptive compact subsets and their relation to renorming problems.

Descriptive properties of mappings between nonseparable Luzin spaces

Petr Holický, Václav Komínek (2007)

Czechoslovak Mathematical Journal

We relate some subsets G of the product X × Y of nonseparable Luzin (e.g., completely metrizable) spaces to subsets H of ℕ ℕ × Y in a way which allows to deduce descriptive properties of G from corresponding theorems on H . As consequences we prove a nonseparable version of Kondô’s uniformization theorem and results on sets of points y in Y with particular properties of fibres f - 1 ( y ) of a mapping f X → Y . Using these, we get descriptions of bimeasurable mappings between nonseparable Luzin spaces in terms of fibres.

Descriptive Sets and the Topology of Nonseparable Banach Spaces

Hansell, R. (2001)

Serdica Mathematical Journal

This paper was extensively circulated in manuscript form beginning in the Summer of 1989. It is being published here for the first time in its original form except for minor corrections, updated references and some concluding comments.

Devil's staircase route to chaos in a forced relaxation oscillator

Lluis Alsedà, Antonio Falcó (1994)

Annales de l'institut Fourier

We use one-dimensional techniques to characterize the Devil’s staircase route to chaos in a relaxation oscillator of the van der Pol type with periodic forcing term. In particular, by using symbolic dynamics, we give the behaviour for certain range of parameter values of a Cantor set of solutions having a certain rotation set associated to a rational number. Finally, we explain the phenomena observed experimentally in the system by Kennedy, Krieg and Chua (in [10]) related with the appearance of...

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