The search session has expired. Please query the service again.
Displaying 41 –
60 of
151
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 and 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...
Transformations T:[0,1] → [0,1] with two monotonic pieces are considered. Under the assumption that T is topologically transitive and , it is proved that the invariant measures concentrated on periodic orbits are dense in the set of all invariant probability measures.
We study the class of descriptive compact spaces, the Banach spaces generated by descriptive compact subsets and their relation to renorming problems.
We relate some subsets of the product of nonseparable Luzin (e.g., completely metrizable) spaces to subsets of in a way which allows to deduce descriptive properties of from corresponding theorems on . As consequences we prove a nonseparable version of Kondô’s uniformization theorem and results on sets of points in with particular properties of fibres of a mapping . Using these, we get descriptions of bimeasurable mappings between nonseparable Luzin spaces in terms of fibres.
We study the descriptive set theoretical complexity of various randomness notions.
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.
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...
Currently displaying 41 –
60 of
151