Richness of chaotic dynamics in nonholonomic models of a Celtic stone
From MaRDI portal
Publication:2449284
DOI10.1134/S1560354713050055zbMath1417.37222MaRDI QIDQ2449284
Alexey O. Kazakov, A. S. Gonchenko, Sergey V. Gonchenko
Publication date: 7 May 2014
Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)
strange attractorCeltic stonemixed dynamicsdiscrete Lorenz attractornonholonomic modelShilnikov-like spiral attractor
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Nonholonomic systems related to the dynamics of a system of particles (70F25) Dynamical aspects of attractors and their bifurcations (37G35) Nonholonomic dynamical systems (37J60)
Related Items
On discrete homoclinic attractors of three-dimensional diffeomorphisms, Spiral chaos in the nonholonomic model of a Chaplygin top, On \(1:3\) resonance under reversible perturbations of conservative cubic Hénon maps, On the birth of discrete Lorenz attractors under bifurcations of 3D maps with nontransversal heteroclinic cycles, Constructing chaotic repellors, Verification of hyperbolicity for attractors of some mechanical systems with chaotic dynamics, Topology and Bifurcations in Nonholonomic Mechanics, Elements of Contemporary Theory of Dynamical Chaos: A Tutorial. Part I. Pseudohyperbolic Attractors, The phenomenon of reversal in the Euler-Poincaré-Suslov nonholonomic systems, Simple Scenarios of Onset of Chaos in Three-Dimensional Maps, Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach, On three types of dynamics and the notion of attractor, On some simple examples of mechanical systems with hyperbolic chaos, Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics, On the Chaotic Dynamics Associated with the Center Manifold Equations of Double-Diffusive Convection Near a Codimension-Four Bifurcation Point at Moderate Thermal Rayleigh Number, Three types of attractors and mixed dynamics of nonholonomic models of rigid body motion, On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators, Variety of strange pseudohyperbolic attractors in three-dimensional generalized Hénon maps, The reversal and chaotic attractor in the nonholonomic model of Chaplygin's top, Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model, Roller racer with varying gyrostatic momentum: acceleration criterion and strange attractors, Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors, Understanding reversals of a rattleback, Unnamed Item, Kantorovich–Rubinstein–Wasserstein distance between overlapping attractor and repeller, Strange attractors and mixed dynamics in the problem of an unbalanced rubber ball rolling on a plane, The third type of chaos in a system of two adaptively coupled phase oscillators, Homoclinic tangencies to resonant saddles and discrete Lorenz attractors, Dynamics of rubber Chaplygin sphere under periodic control, Unnamed Item, Reversible perturbations of conservative Hénon-like maps, Breakdown of symmetry in reversible systems, Asymptotically exact codimension-four dynamics and bifurcations in two-dimensional thermosolutal convection at high thermal Rayleigh number: chaos from a quasi-periodic homoclinic explosion and quasi-periodic intermittency, A parabolic Chaplygin pendulum and a Paul trap: nonintegrability, stability, and boundedness, The Chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration, Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points, On the intersection of a chaotic attractor and a chaotic repeller in the system of two adaptively coupled phase oscillators, Analytical solutions of the Lorenz system, The dynamics and control of a spherical robot with an internal omniwheel platform, Dynamics and control of an omniwheel vehicle, From chaos to quasi-periodicity, Regular and chaotic dynamics of a Chaplygin sleigh due to periodic switch of the nonholonomic constraint, Topaj-Pikovsky involution in the Hamiltonian lattice of locally coupled oscillators, Bifurcations and Chaos in the Dynamics of Two Point Vortices in an Acoustic Wave, Merger of a Hénon-like attractor with a Hénon-like repeller in a model of vortex dynamics, Motion of a smooth foil in a fluid under the action of external periodic forces. I., Emergence and synchronization of a reversible core in a system of forced adaptively coupled Kuramoto oscillators, Motion of a smooth foil in a fluid under the action of external periodic forces. II, Fermi-like acceleration and power-law energy growth in nonholonomic systems, Wild pseudohyperbolic attractor in a four-dimensional Lorenz system, On scenarios of the onset of homoclinic attractors in three-dimensional non-orientable maps, A criterion for mixed dynamics in two-dimensional reversible maps, Lorenz- and Shilnikov-Shape Attractors in the Model of Two Coupled Parabola Maps, On discrete Lorenz-like attractors
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
- Small random perturbations of dynamical systems and the definition of attractors
- High dimension diffeomorphisms displaying infinitely many periodic attractors
- Dynamical phenomena occurring due to phase volume compression in nonholonomic model of the rattleback
- Diffeomorphisms with infinitely many sinks
- Prolongations and stability in dynamical systems
- Strange attractors and mixed dynamics in the problem of an unbalanced rubber ball rolling on a plane
- On Lorenz-like attractors in model of celtic stone
- An example of a wild strange attractor
- Newhouse regions for reversible systems with infinitely many stable, unstable and elliptic periodic orbits
- Persistence of homoclinic tangencies in higher dimensions
- Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps
- Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps
- Examples of Lorenz-like Attractors in Hénon-like Maps
- THREE-DIMENSIONAL HÉNON-LIKE MAPS AND WILD LORENZ-LIKE ATTRACTORS