Metric with ergodic geodesic flow is completely determined by unparameterized geodesics.
Minimal tori in S4.
Minkowski Plane, Confocal Conics, and Billiards
Models for quadratic algebras associated with second order superintegrable systems in 2D.
Multi-Hamiltonian structures on Beauville's integrable system and its variant.
Multiple Hamiltonian structures for the Ishii's equation.
Multiplicative integrable models from Poisson-Nijenhuis structures
We discuss the role of Poisson-Nijenhuis (PN) geometry in the definition of multiplicative integrable models on symplectic groupoids. These are integrable models that are compatible with the groupoid structure in such a way that the set of contour levels of the hamiltonians in involution inherits a topological groupoid structure. We show that every maximal rank PN structure defines such a model. We consider the examples defined on compact hermitian symmetric spaces studied by F. Bonechi, J. Qiu...