Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Koiller, Jair"'
On the interplay between vortices and harmonic flows: Hodge decomposition of Euler's equations in 2d
Let $\Sigma$ be a compact manifold without boundary whose first homology is nontrivial. Hodge decomposition of the incompressible Euler's equation in terms of 1-forms yields a coupled PDE-ODE system. The $L^2$-orthogonal components are a `pure' vorti
Externí odkaz:
http://arxiv.org/abs/2309.12582
We compare invariants of N-periodic trajectories in the elliptic billiard, classic and new, to their aperiodic counterparts via a spatial integrals evaluated over the boundary of the elliptic billiard. The integrand is weighed by a universal measure
Externí odkaz:
http://arxiv.org/abs/2102.10899
Publikováno v:
Arnold Mathematical Journal volume 7, pages 341-355, 2021
We introduce several-dozen experimentally-found invariants of Poncelet N-periodics in the confocal ellipse pair (Elliptic Billiard). Recall this family is fully defined by two integrals of motion (linear and angular momentum), so any "new" invariants
Externí odkaz:
http://arxiv.org/abs/2004.12497
Publikováno v:
Journal for Geometry and Graphics, Volume 24 No. 1, 79-101, 2020
The dynamic geometry of the family of 3-periodics in the Elliptic Billiard is mystifying. Besides conserving perimeter and the ratio of inradius-to-circumradius, it has a stationary point. Furthermore, its triangle centers sweep out mesmerizing loci
Externí odkaz:
http://arxiv.org/abs/2002.00001
New invariants in the one-dimensional family of 3-periodic orbits in the elliptic billiard were introduced by the authors in "Can the Elliptic Billiard Still Surprise Us?" (2020), Math. Intelligencer, 42(1): 6--17, some of which were generalized to $
Externí odkaz:
http://arxiv.org/abs/2001.08054
A triangle center such as the incenter, barycenter, etc., is specified by a function thrice- and cyclically applied on sidelengths and/or angles. Consider the 1d family of 3-periodics in the elliptic billiard, and the loci of its triangle centers. So
Externí odkaz:
http://arxiv.org/abs/2001.08041
Publikováno v:
Math Intelligencer 42, 6-17, 2020
Can any secrets still be shed by that much studied, uniquely integrable, Elliptic Billiard? Starting by examining the family of 3-periodic trajectories and the loci of their Triangular Centers, one obtains a beautiful and variegated gallery of curves
Externí odkaz:
http://arxiv.org/abs/1911.01515
Publikováno v:
Journal of Geometric Mechanics, Volume 9, Number 3, September 2017, pp. 257290
In this paper, we study simple splines on a Riemannian manifold $Q$ from the point of view of the Pontryagin maximum principle (PMP) in optimal control theory. The control problem consists in finding smooth curves matching two given tangent vectors w
Externí odkaz:
http://arxiv.org/abs/1711.02773
Akademický článek
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Publikováno v:
Anais da Academia Brasileira de Ciencias 73 (2) 165 (2001)
In this note we revisit E. Cartan's address at the 1928 International Congress of Mathematicians at Bologna, Italy. The distributions considered here will be of the same class as those considered by Cartan, a special type which we call strongly non-h
Externí odkaz:
http://arxiv.org/abs/1110.1356