Bifurcations of limit cycles of perturbed completely integrable systems
The main purpose of this article is to study from the geometric point of view the problem of limit cycles bifurcation of perturbed completely integrable systems.
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arXiv subjects
Răzvan M. Tudoran
Publications and source records attributed to Răzvan M. Tudoran.
Complete integrability versus symmetry
The purpose of this article is to show that on an open and dense set, complete integrability implies the existence of symmetry.
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On a unified formulation of completely integrable systems
The purpose of this article is to show that a $\mathcal{C}^1$ differential system on $\R^n$ which admits a set of $n-1$ independent $\mathcal{C}^2$ conservation laws defined on an open subset $Ω\subseteq \R^n$, is essentially $\mathcal{C}^1$ equivalent on an open and dense subset of $Ω$, with the linear differential system $u^\prime_1=u_1, \ u^\prime_2=u_2,..., \ u^\prime_n=u_n$. The main results are illustrated in the case of two concrete dynamical systems, namely the three dimensional Lotka-Volterra system, and respectively the Euler equations from the free rigid body dynamics.
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On a class of three dimensional quadratic Hamiltonian systems
The purpose of this article is to compute the normal form of a class of general quadratic Hamiltonian systems that generalizes naturally Euler's equations from the free rigid body dynamics.
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On a Hamiltonian version of a 3D Lotka-Volterra system
In this paper we present some relevant dynamical properties of a 3D Lotka-Volterra system from the Poisson dynamics point of view.
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