Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation

Approximate Solutions and Symmetry of a Two-Component Nonlocal Reaction-Diffusion Population Model of the Fisher–KPP Type

“…Following [23], we present the solution of the Cauchy problem (38) and (39) in terms of the evolution operator of Equation (39) for the initial function ϕ(x) belonging to the class P D 1 0 defined by (19).…”

The Hojman Construction and Hamiltonization of Nonholonomic Systems

“…As a result, the symplectic leaf can be immersed in the phase space in a fairly complicated (in particular, chaotic) way, and the above-described picture is not always realized. Nevertheless, the above Poisson structure turns out to be useful for the investigation of stability problems [29].…”

Topology and Bifurcations in Nonholonomic Mechanics

“…In our particular case, the variables Ω 1 , Ω 2 , ω 1 , ω 2 , ω 3 correspond to (more precisely, are dual 1 All Poisson brackets of rank two are described in a recent paper by A. Yu. Konyaev [Konyaev, 2014]. The issue of classification of such brackets was raised in [Bolsinov et al, 2012], where the following question was also formulated: "Are there any Hamiltonian systems with brackets that do not admit globally defined independent n − 1 integrals?".…”

“…They have appeared in various contexts and studied, for example, in [Bolsinov & Taimanov, 2000a,b;Konyaev, 2014;Butler, 2003]. Their main property is that they are of rank two 1 .…”

“…, x 4 ) we consider the n-dimensional vector x ∈ R n . The following statement summarizes the basic properties of Lie algebras of the type under consideration and the related Poisson brackets, which can be useful for applications (see also [Konyaev, 2014] …”