The invariant manifolds of systems with first integrals

Invariant critical sets of conserved quantities

“…As a consequence we will obtain the following well known result which was applied for studying invariant sets of various mechanical systems, see for example [6].…”

Dynamics under Geometric Dissipation

“…The subsets G * and Y are also invariant subsets for the perturbed dynamics. Indeed, G * is invariant under the unperturbed dynamic (see [4], [8]) and if x ∈ G * is an initial condition then x p (t, x) = x un (t, x) ∈ G * for all t ∈ R, which implies that G * is invariant under the perturbed dynamics. Consequently, Y is also an invariant set for the perturbed dynamics.…”

On motions of a conservative system on invariant manifolds

“…

In [Irtegov and Burlakova, 2017], the algorithms for the qualitative analysis of conservative systems have been presented. These are based on the Routh-Lyapunov method [Lyapunov, 1954] and some its modifications [Irtegov and Titorenko, 2009] as well as computer algebra methods [Cox, Little, and O'Shea, 1997]. In the paper proposed, the application of the algorithms is demonstrated by analysing a conservative system, the study of which is also of interest.

…”