Call for papers

Call for Papers: Special Issue dedicated to the 175th Birthday of Sofya Kovalevskaya

The issue will include papers showing a wide range of modern research related to the areas that were influenced by S. Kovalevskaya, and will emphasize the following topics which are also central subjects of RCD. The deadline for submission of manuscripts is June 15, 2025. Publication of the issue is provisionally scheduled for September 2025.

Call for Papers: Special Issue dedicated to the memory of Alexey V. Borisov

The special issue will emphasize the topics greatly influenced by A. V. Borisov which are also central subjects of Regular and Chaotic Dynamics. The deadline for submission of manuscripts is August 1, 2025. Publication of the issue is provisionally scheduled for November 2025.


Volume 30, Number 3

Kurakin L. G.,  Ostrovskaya I. V.,  Sokolovskiy M. A.
Abstract
A two-layer quasigeostrophic model is considered in the $f$-plane approximation. The stability of a discrete axisymmetric vortex structure is analyzed for the case where the structure consists of a central vortex of arbitrary effective intensity $\Gamma$ and $N$ ($N = 4, 5$ and $6$) identical peripheral vortices. The identical vortices, each having a unit effective intensity, are uniformly distributed over a circle of radius $R$ in the lower layer. The central vortex lies either in the same or in another layer. The problem has three parameters $(R,\Gamma,\alpha)$, where $\alpha$ is the difference between layer nondimensional thicknesses. The cases $N=2, 3$ were investigated by us earlier.
The theory of stability of steady-state motions of dynamical systems with a continuous symmetry group $\mathcal{G}$ is applied. The two definitions of stability used in the study are Routh stability and $\mathcal{G}$-stability. The Routh stability is the stability of a one-parameter orbit of a steady-state rotation of a vortex structure, and the $\mathcal{G}$-stability is the stability of a three-parameter invariant set $O_{\mathcal{G}}$, formed by the orbits of a continuous family of steady-state rotations of a two-layer vortex structure. The problem of Routh stability is reduced to the problem of stability of a family of equilibria of a Hamiltonian system. The quadratic part of the Hamiltonian and the eigenvalues of the linearization matrix are studied analytically.
The results of theoretical analysis are sustained by numerical calculations of vortex trajectories.
Keywords: discrete vortex structure, two-layer rotating fluid, stability
Citation: Kurakin L. G.,  Ostrovskaya I. V.,  Sokolovskiy M. A., On the Stability of Discrete $N + 1$ Vortices in a Two-Layer Rotating Fluid: The Cases $N = 4, 5, 6$, Regular and Chaotic Dynamics, 2025, vol. 30, no. 3, pp. 325-353
DOI:10.1134/S1560354724580019
Costa-Villegas M.,  García-Naranjo L. C.
Abstract
We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body that rolls without slipping on the plane. These examples are constructed by taking as given two vector fields, one on the surface of the body and another on the plane, which specify the velocity of the contact point. We investigate dynamical aspects of the system such as existence of first integrals, smooth invariant measure, integrability and chaotic behavior, giving special attention to special shapes of the convex body and specific choices of the vector fields for which the affine nonholonomic constraints may be physically realized.
Keywords: nonholonomic systems, rigid body dynamics, first integrals, invariant measure, integrability, chaotic behavior
Citation: Costa-Villegas M.,  García-Naranjo L. C., Affine Generalizations of the Nonholonomic Problem of a Convex Body Rolling without Slipping on the Plane, Regular and Chaotic Dynamics, 2025, vol. 30, no. 3, pp. 354-381
DOI:10.1134/S1560354725510021
van der Kamp P. H.,  McLaren D. I.,  Quispel G. R. W.
Abstract
We study a class of integrable inhomogeneous Lotka – Volterra systems whose quadratic terms are defined by an antisymmetric matrix and whose linear terms consist of three blocks. We provide the Poisson algebra of their Darboux polynomials and prove a contraction theorem. We then use these results to classify the systems according to the number of functionally independent (and, for some, commuting) integrals. We also establish separability/solvability by quadratures, given the solutions to the 2- and 3-dimensional systems, which we provide in terms of the Lambert $W$ function.
Keywords: Poisson algebra, integrability, Lotka – Volterra system, Lambert $W$ function, Darboux polynomial
Citation: van der Kamp P. H.,  McLaren D. I.,  Quispel G. R. W., On a Quadratic Poisson Algebra and Integrable Lotka – Volterra Systems with Solutions in Terms of Lambert’s $W$ Function, Regular and Chaotic Dynamics, 2025, vol. 30, no. 3, pp. 382-407
DOI:10.1134/S1560354724580032
Broer H. W.,  Hanßmann H.,  Wagener F. O.
Abstract
Kolmogorov – Arnold – Moser theory started in the 1950s as the perturbation theory for persistence of multi- or quasi-periodic motions in Hamiltonian systems. Since then the theory obtained a branch where the persistent occurrence of quasi-periodicity is studied in various classes of systems, which may depend on parameters. The view changed into the direction of structural stability, concerning the occurrence of quasi-periodic tori on a set of positive Hausdorff measure in a sub-manifold of the product of phase space and parameter space. This paper contains an overview of this development with an emphasis on the world of dissipative systems, where families of quasi-periodic tori occur and bifurcate in a persistent way. The transition from orderly to chaotic dynamics here forms a leading thought.
Keywords: quasi-periodic invariant tori, KAM theory, persistence, bifurcations
Citation: Broer H. W.,  Hanßmann H.,  Wagener F. O., Parametrised KAM Theory, an Overview, Regular and Chaotic Dynamics, 2025, vol. 30, no. 3, pp. 408-450
DOI:10.1134/S156035472551001X
Surov M. O.,  Grigorov M. Y.
Abstract
This paper is devoted to the servoconstraints approach in the problem of periodic motion planning for Euler – Lagrange systems with a single degree of underactuation. We focus on the case where the servoconstraint is not regular and thus leads to the appearance of isolated singularities in reduced dynamics. We demonstrate that, subject to supplementary conditions, the reduced dynamics possess smooth solutions that pass through the singular point and this can be utilized for finding trajectories of the original system. Building upon this outcome, we solve the problem of motion planning of the Pendubot system with an imposed eight-shaped servoconstraint. To verify the feasibility of the discovered trajectory, we present computer simulation results of the closed-loop system with feedback that enables orbital stabilization for the trajectory.
Keywords: mechanical systems, virtual holonomic constraints, servoconstraints, motion planning
Citation: Surov M. O.,  Grigorov M. Y., Closed Servoconstraints in Periodic Motion Planning for Underactuated Mechanical Systems, Regular and Chaotic Dynamics, 2025, vol. 30, no. 3, pp. 451-462
DOI:10.1134/S1560354725030013