相关论文: Precession of the Kovalevskaya and Goryachev-Chapl…

In this paper, we study the topology of the Liouville foliation of an analogue of the Kovalevskaya integrable case on the Lie algebra so(3; 1). The Fomenko-Zieschang invariants (i.e., marked molecules) of a given foliation on each regular…

The general integrability cases in the rigid-body dynamics are the solutions of Lagrange, Euler, Kovalevskaya, and Goryachev-Chaplygin. The first two can be included in Smale's scheme for studying the phase topology of natural systems with…

In this paper we study topological properties of an integrable case for Euler's equations on the Lie algebra $\textrm{so}(4)$, which can be regarded as an analogue of the classical Kovalevskaya case in rigid body dynamics. In particular,…

Topology of Liouville foliations for an analogue of the Kovalevskaya integrable case on Lie algebra so(4) is discussed. Fomenko-Zieschang invariants (i.e. marked molecules) were calculated for these foliations on every regular isoenergy…

We describe a new type of top, the twisted top, obtained by appending a cocycle to the Lie-Poisson bracket for the charged heavy top, thus breaking its semidirect product structure. The twisted top has an integrable case that corresponds to…

The structure of integral manifolds in the Kovalevskaya problem of the motion of a heavy rigid body about a fixed point is considered. An analytic description of a bifurcation set is obtained, and bifurcation diagrams are constructed. The…

The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of $v/c$, important differences in the predicted angle of precession appear, depending on the…

The book contains the results obtained by the author in 1975-1982 and presents new constructive methods of the topological analysis of integrable systems having non-linear integrals in involution. The phase topology of the classical…

In the paper we determine the class of diffeomorphism of three-dimensional regular common level surfaces of Hamiltonian and Casimir functions for the analog of Kovalevskaya case on Lie algebra $\textrm{so}(4)$. We start from…

Asymptotic behaviour of a tippe top, under the action of gliding friction. Liapunov stability analysis of the asymptotics of states with arbitrary initial conditions.

The covariant Lyapunov analysis is generalised to systems attached to deterministic thermal reservoirs that create a heat current across the system and perturb it away from equilibrium. The change in the Lyapunov exponents as a function of…

We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci (J. Math. Phys. 37, 1772-1775 (1996)) is…

We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize…

Several algorithms are presented for the accurate computation of the leaves in the foliation of an ODE near a hyperbolic fixed point. They are variations of a contraction mapping method in [25] to compute inertial manifolds, which…

We introduce a curvature atlas for left-invariant metrics on SU(2), based on the inertial curvature field derived from the Euler-Poincare equations. We prove that the classical integrable cases of the heavy top--spherical, Lagrange,…

This work deals with the dynamics of a class of stochastic dynamical systems with a multiplicative non-Gaussian Levy noise. We first establish the existence of stable and unstable foliations for this system via the Lyapunov-Perron method.…

In this paper we consider a completely Liouville integrable Hamiltonian system with two degrees of freedom, which describes the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a cylindrical trap. For vortex pairs…

In this paper we present a generalization of the Goryachev-Chaplygin integrable case on a bundle of Poisson brackets, and on Sokolov terms in his new integrable case of Kirchhoff equations. We also present a new analogous integrable case…

A model for the dynamics of actin filament ends along the leading edge of the lamellipodium is analyzed. It contains accounts of nucleation by branching, of deactivation by capping, and of lateral flow along the leading edge by…

We study analytic deformations of holomorphic differential 1-forms. The initial 1-form is exact homogeneous and the deformation is by polynomial integrable 1-forms. We investigate under which conditions the elements of the deformation are…