42 citations · 151 across the 15 of their papers we have counts for
16 papers
Conformally symplectic Chaplygin reduction in rubber rolling of surfaces of revolution over the plane
Jair Koiller
Rubber rolling (no-slip and no-twist) of a convex body on the plane under the influence of gravity is a SE(2) Chaplygin system, that reduces to the sphere of Poisson vectors. I com…
Vortices for lake equations (review with questions and speculations)
Jair Koiller
The `lake equation' on a planar domain D with bathymetry b(x,y) is given by $ \partial_t u + (u \cdot {\rm grad}) u= -{\rm grad}\, p \,, \,\,{\rm div} (b u) = 0 \,,\, \text{with}\,…
On the interplay between vortices and harmonic flows: Hodge decomposition of Euler's equations in 2d
Clodoaldo Grotta-Ragazzo, Björn Gustafsson, Jair Koiller
Let 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 P…
Average Elliptic Billiard Invariants with Spatial Integrals
Jair Koiller, Dan Reznik, Ronaldo Garcia
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 t…
Eighty New Invariants of N-Periodics in the Elliptic Billiard
Dan Reznik, Ronaldo Garcia, Jair Koiller
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 inte…
The Ballet of Triangle Centers on the Elliptic Billiard
Dan Reznik, Ronaldo Garcia, Jair Koiller
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 stationar…