Robin J. DEELEY †, Joshua T. HORWOOD ‡, Raymond G. MCLENAGHAN † and Roman G. SMIRNOV § † Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada E-mail:… (More)

The term “manifold of n dimensions” in this setting describes a set of n variables that independently take on the real values from −∞ to ∞ ([12], p 116). Motivated by this idea, one can assert that… (More)

The well-known problem of classical mechanics considered by Bertrand (1857) and Darboux (1901) is reviewed in the context of Cartan’s geometry. UDK: 514.85; MSC: 37J35, 53C05

Orthogonal separability of finite-dimensional Hamiltonians is characterized by using various geometrical concepts, including Killing tensors, moving frames, the Nijenhuis tensor, bi-Hamiltonian and… (More)

We show that the three body Calogero model with inverse square potentials can be interpreted as a maximally superintegrable and multiseparable system in Euclidean three-space. As such it is a special… (More)

The invariant theory of Killing tensors (ITKT) is extended by introducing the new concepts of covariants and joint invariants of (product) vector spaces of Killing tensors defined in… (More)

The theory of bi-Hamiltonian systems has its roots in what is commonly referred to as the “Lenard recursion formula”. The story about the discovery of the formula told by Andrew Lenard is the subject… (More)

Dependence of the damping rate of the oscillations of the dust particles levitating in the sheath on the plasma parameters is investigated both theoretically and experimentally. Significant… (More)

We present a method of generating Magri-Morosi-Gel'fand-Dorfman's (MMGD) bi-Hamiltonian structure leading to complete integrability of the associated Hamilto-nian system and discuss its applicability… (More)

The interplay between the Hamilton–Jacobi theory of orthogonal separation of variables and the theory of group actions is investigated based on concrete examples.