Related papers: Convergent Normal Forms of Symmetric Dynamical Sys…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra,…
We identify a generic class of two dimensional nonstandard Hamiltonian systems which exhibit isochronous behaviour. This class of systems belongs to the two dimensional mixed Li\'enard- type equations and is obtained by generalizing the…
It is shown, that the geometrical objects of Batalin-Vilkovisky formalism-- odd symplectic structure and nilpotent operator $\Delta$ can be naturally uncorporated in Duistermaat--Heckman localization procedure. The presence of the…
The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and…
The existence of point symmetries in the cosmological field equations of generalized vacuum scalar--tensor theories is considered within the context of the spatially homogeneous cosmologies. It is found that such symmetries only occur in…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
Using homogeneous dynamical approach, we obtain a complete description of the forms with discrete set of values at the integer points and not representing zero non-trivially over the rational numbers. As a consequence, we obtain a general…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
The term integrable asymptotically conformal at a point for a quasiconformal map defined on a domain is defined. Furthermore, we prove that there is a normal form for this kind attracting or repelling or super-attracting fixed point with…
This paper shows that various relevant dynamical systems can be described as vector fields associated to smooth functions via a bracket that defines what we call a Leibniz structure. We show that gradient flows, some dissipative systems,…
The dynamical (super)symmetries for various monopole systems are reviewed. For a Dirac monopole, no smooth Runge-Lenz vector can exist; there is, however, a spectrum-generating conformal $o(2,1)$ dynamical symmetry that extends into…
The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force…
We show that partial dynamical symmetries (PDS) can occur at critical-points of quantum phase transitions, in which case, underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several…
Newtonian, Lagrangian, and Hamiltonian dynamical systems are well formalized mathematically. They give rise to geometric structures describing motion of a point in smooth manifolds. Riemannian metric is a different geometric structure…
We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the…
Pseudo-harmonic morphisms give rise on the domain space to a distribution which admits an almost complex structure compatible with the given Riemannian metric. We shall show that this property, together with the harmonicity, are preserved…