We give an overview of some new and old results on geometric properties of eigenfunctions
of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical …

We give a uniform lower bound for the polynomial complexity of Reeb flows on the
spherization (S* M, ξ) over a closed manifold. Our measure for the dynamical complexity of …

Consider a point moving on M and let γ (t) be its trajectory. According to the second Newton
law, its motion is defined by the equation ma= F. What is the meaning of the acceleration a in …

This is a survey on finite-dimensional integrable dynamical systems related to Hamiltonian $
G $-actions. Within a framework of noncommutative integrability we study integrability of $ G …

This paper has four main results:(i) it shows that left-invariant geodesic flows on a broad
class of two-step nilmanifolds—which are dubbed almost non-singular—are integrable in …

INTEGRABLE GEODESIC FLOWS ON RIEMANNIAN MANIFOLDS AV Bolsinov UDC 514.764.2
Page 1 Journal of Mathematical Sciences, Vol. 123, No. 4, 2004 INTEGRABLE GEODESIC …

Let (Σ, g) be a compact C2 finslerian 3-manifold. If the geodesic flow of g is completely
integrable, and the singular set is a tamely-embedded polyhedron, then π1 (Σ) is almost …

We introduce the polynomial Hamiltonian [Formula: see text] and we prove that the
associated Hamiltonian system is Liouville-C∞-integrable, but fails to be real-analytically …

The connections between Euler's equations on central extensions of Lie algebras and
Euler's equations on the original, extended algebras are described. A special infinite …

The concept of an F-structure was introduced by M. Gromov in [16] as a natural
generalization of a torus action on a manifold. Then J. Cheeger and Gromov [16, 8, 9] …