Search results for " Birkhoff"
showing 5 items of 5 documents
Dehn surgeries and smooth structures on 3-dimensional transitive Anosov flows.
2020
The present thesis is about Dehn surgeries and smooth structures associated with transitive Anosov flows in dimension three. Anosov flows constitute a very important class of dynamical systems, because of its persistent chaotic behaviour, as well as for its rich interaction with the topology of the ambient space. Even if a lot is known about the dynamical and ergodic properties of these systems, there is not a clear understanding about how to classify its different orbital equivalence classes. Until now, the biggest progress has been done in dimension three, where there is a family of techniques intended for the construction of Anosov flows called surgeries.During the realization of this th…
Vortex layers of small thickness
2020
We consider a 2D vorticity configuration where vorticity is highly concentrated around a curve and exponentially decaying away from it: the intensity of the vorticity is $O(1/epsilon)$ on the curve while it decays on an $O(epsilon)$ distance from the curve itself. We prove that, if the initial datum is of vortex-layer type, Euler solutions preserve this structure for a time which does not depend on $epsilon$. Moreover the motion of the center of the layer is well approximated by the Birkhoff-Rott equation.
Regularized Euler-alpha motion of an infinite array of vortex sheets
2016
We consider the Euler- $$\alpha $$ regularization of the Birkhoff–Rott equation and compare its solutions with the dynamics of the non regularized vortex-sheet. For a flow induced by an infinite array of planar vortex-sheets we analyze the complex singularities of the solutions.Through the singularity tracking method we show that the regularized solution has several complex singularities that approach the real axis. We relate their presence to the formation of two high-curvature points in the vortex sheet during the roll-up phenomenon.
Some new results on integration for multifunction
2018
It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable.
Measures of Fuzziness and Information: some challenges from reflections on aesthetic experience
2011
Evaluating aesthetic in arts is, by sheer consensus, a daunting task. Even when all the social, historic and politic considerations are stripped from the living flesh of the piece – and with them most of what differentiates creation from description – the folk concept that beauty stems from some sort of order/chaos relationship, formalized by G. D. Birkhoff as the aesthetic measure, requires an adequate and consistent quantification of both factors. Old and new approaches to the problem generally resort to classical definitions of information and entropy (Shannon entropy, Kolmogorov-Solomonoff complexity) and their derivatives, neglecting the fact that compactness and repetition have a diff…