The Dynamics of Rabinovich system
The paper presents some dynamical aspects of Rabinovich type, with distributed delay and with fractional derivatives.
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arXiv subjects
Mircea Puta
Publications and source records attributed to Mircea Puta.
Asymptotic Stability for a Class of Metriplectic Systems
Using the framework of metriplectic systems on $\R^n$ we will describe a constructive geometric method to add a dissipation term to a Hamilton-Poisson system such that any solution starting in a neighborhood of a nonlinear stable equilibrium converges towards a certain invariant set. The dissipation term depends only on the Hamiltonian function and the Casimir functions.
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Periodic orbits in the case of a zero eigenvalue
We will show that if a dynamical system has enough constants of motion then a Moser-Weinstein type theorem can be applied for proving the existence of periodic orbits in the case when the linearized system is degenerate.
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Equivalence of energy methods in stability theory
We will prove the equivalence of three methods, the so called energy methods, for establishing the stability of an equilibrium point for a dynamical system. We will illustrate by examples that this result simplifies enormously the amount of computations especially when the stability can not be decided with one of the three methods.
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On the symmetry breaking phenomenon
We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems. We give sufficient conditions for symmetry breaking in both cases.
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Symmetry breaking for toral actions in simple mechanical systems
For simple mechanical systems, bifurcating branches of relative equilibria with trivial symmetry from a given set of relative equilibria with toral symmetry are found. Lyapunov stability conditions along these branches are given.
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Controllability of reduced systems
Sufficient conditions for the controllability of a conservative reduced system are given. Several examples illustrating the theory are also presented.
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A short proof of chaos in an atmospheric system
We will prove the presence of chaotic motion in the Lorenz five-component atmospheric system model using the Melnikov function method developed by Holmes and Marsden for Hamiltonian systems on Lie Groups.
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