0
2013
Impact Factor

Volume 6, Number 2

Volume 6, Number 2, 2001

Russmann H.
Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems
Abstract
Invariant tori for analytic nearly integrable Hamiltonian systems are constructed under rather weak sufficient conditions being even necessary in the case of maximal invariant tori. All small devisors are controlled by a general approximation function the properties of which correspond to the Bruno condition in analytic problems near a singular point. The admitted size of the perturbations is numerically determined in numerically given systems.
Citation: Russmann H., Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems, Regular and Chaotic Dynamics, 2001, vol. 6, no. 2, pp. 119-204
DOI:10.1070/RD2001v006n02ABEH000169
Leboeuf P.,  Monastra A. G.,  Bohigas O.
The Riemannium
Abstract
The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up to a Fermi energy $E_F$. The distribution of the total energy is shown to be non-Gaussian, asymmetric and independent of $E_F$ in the limit $E_F \to\infty$. The moments of the limit distribution are computed analytically. The autocorrelation function, the finite energy corrections, and a comparison with random matrix theory are also discussed.
Citation: Leboeuf P.,  Monastra A. G.,  Bohigas O., The Riemannium, Regular and Chaotic Dynamics, 2001, vol. 6, no. 2, pp. 205-210
DOI:10.1070/RD2001v006n02ABEH000170
Kasman A.
Finite Canonical Commutation Relations and the Rational Nested Bethe Ansatz
Abstract
Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the "completed Calogero–Moser phase space" of matrices which satisfy a finite dimensional analogue of the canonical commutation relationship. A key feature is the fact that the RNBA equations are derived only from this commutation relationship and some elementary linear algebra. The solutions constructed in this way inherit continuous and discrete symmetries from the CM phase space.
Citation: Kasman A., Finite Canonical Commutation Relations and the Rational Nested Bethe Ansatz, Regular and Chaotic Dynamics, 2001, vol. 6, no. 2, pp. 211-214
DOI:10.1070/RD2001v006n02ABEH000171
Letelier P. S.,  Motter A. E.
Arbitrariness in Defining Fractal Basins: Relations Between Open and Closed Systems
Abstract
A discussion about dependences of the (fractal) basin boundary dimension with the definition of the basins and the size of the exits is presented for systems with one or more exits. In particular, it is shown that the dimension is largely independent of the choice of the basins, and decreases with the size of the exits. Considering the limit of small exits, a strong relation between fractals in exit systems and chaos in closed systems is found. The discussion is illustrated by simple examples of one-dimensional maps.
Citation: Letelier P. S.,  Motter A. E., Arbitrariness in Defining Fractal Basins: Relations Between Open and Closed Systems, Regular and Chaotic Dynamics, 2001, vol. 6, no. 2, pp. 215-226
DOI:10.1070/RD2001v006n02ABEH000172
Kuleshov A. S.
On the Generalized Chaplygin Integral
Abstract
The problem of the motion of a rotational symmetric rigid body along a perfectly rough surface is considered. The conditions of existence of a Chaplygin-type integral are obtained. It is shown, that these conditions are valid in the case of the motion of a nonhomogeneous dynamically symmetric sphere along a perfectly rough plane or along the internal surface of a sphere.
Citation: Kuleshov A. S., On the Generalized Chaplygin Integral, Regular and Chaotic Dynamics, 2001, vol. 6, no. 2, pp. 227-232
DOI:10.1070/RD2001v006n02ABEH000173
Kilin A. A.
First Integral in the Problem of Motion of a Circular Cylinder and a Point Vortex in Unbounded Ideal Fluid
Abstract
In the paper Motion of a circular cylinder and a vortex in an ideal fluid (Reg. & Chaot. Dyn. V. 6. 2001. No 1. P. 33-38) Ramodanov S.M. showed the integrability of the problem of motion of a circular cylinder and a point vortex in unbounded ideal fluid. In the present paper we find additional first integral and invariant measure of motion equations.
Citation: Kilin A. A., First Integral in the Problem of Motion of a Circular Cylinder and a Point Vortex in Unbounded Ideal Fluid, Regular and Chaotic Dynamics, 2001, vol. 6, no. 2, pp. 233-234
DOI:10.1070/RD2001v006n02ABEH000174

Back to the list