Results 11 to 20 of about 947,686 (131)
The existences of transverse homoclinic solutions and chaos for parabolic equations [PDF]
, 2007 By using Lyapunov–Schmidt reduction and exponential dichotomies, the persistence of homoclinic orbit is considered for parabolic equations with small perturbations.
C. Zhu, Guang-Ping Luo, Yong-Lu Shu
semanticscholar +2 more sources
Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits [PDF]
, 2008 In this paper we consider the orbital previous termdynamicsnext term of a previous termsolar sailnext term in the Earth-Sun circular restricted three-body problem. The equations of motion of the previous termsailnext term are given by a set of non-linear
Waters, Thomas +3 more
core +4 more sources
Beltrami fields and knotted vortex structures in incompressible fluid flows
Bulletin of the London Mathematical Society, Volume 55, Issue 3, Page 1059-1103, June 2023., 2023 Abstract This paper gives a survey on recent results about the existence of knotted vortex structures in incompressible fluids. This includes the proof of Lord Kelvin's conjecture on the existence of knotted vortex tubes in steady Euler flows and a new probabilistic approach to address Arnold's speculation that typical Beltrami fields should exhibit ...
Alberto Enciso, Daniel Peralta‐Salas
wiley +1 more source
Natural Exponential and Three‐Dimensional Chaotic System
Advanced Science, Volume 10, Issue 15, May 26, 2023., 2023 A novel natural exponential and three‐dimensional chaotic system with higher sensitivity to initial condition is presented. Its characterizations are revealed via various chaotic dynamic indicators. The performance evaluation through recursive and entropy study verifies the model complexity and robustness, while the feasibility of this system is ...
Shiwei Liu +4 more
wiley +1 more source
Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the Three‐Body Problem
Communications on Pure and Applied Mathematics, Volume 76, Issue 3, Page 616-681, March 2023., 2023 Abstract We consider a class of autonomous Hamiltonian systems subject to small, time‐periodic perturbations. When the perturbation parameter is set to zero, the energy of the system is preserved. This is no longer the case when the perturbation parameter is non‐zero.
Maciej J. Capiński, Marian Gidea
wiley +1 more source
The numerical computation of connecting orbits in dynamical systems [PDF]
, 1990 Beyn W-J. The numerical computation of connecting orbits in dynamical systems. IMA Journal of Numerical Analysis. 1990;10(3):379-405.Structural changes in dynamical systems are often related to the appearance or disappearance of orbits connecting two ...
Beyn, Wolf-Jürgen
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International Journal of Mechanical System Dynamics, Volume 3, Issue 1, Page 85-94, March 2023., 2023 Abstract Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems. In this paper, a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Gaussian noise is investigated as an example.
Yong Huang
wiley +1 more source
Symplectomorphisms with positive metric entropy
Proceedings of the London Mathematical Society, Volume 124, Issue 5, Page 691-712, May 2022., 2022 Abstract We obtain a dichotomy for C1$C^1$‐generic symplectomorphisms: either all the Lyapunov exponents of almost every point vanish, or the map is partially hyperbolic and ergodic with respect to volume. This completes a program first put forth by Ricardo Mañé. A key ingredient is an analysis of partially hyperbolic sets of positive volume.
Artur Avila +2 more
wiley +1 more source
Towards global models near homoclinic tangencies of dissipative diffeomorphisms [PDF]
, 1998 A representative model of a return map near homoclinic bifurcation is studied. This model is the so-called fattened Arnold map, a diffeomorphism of the annulus. The dynamics is extremely rich, involving periodicity, quasiperiodicity and chaos. The method
Broer, H; id_orcid +6 more
core +2 more sources
Chaotic Threshold of a Nonlinear Zener Systems Based on the Melnikov Method
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 Regarding a nonlinear Zener model with a viscoelastic Maxwell element as the research object, the complicated dynamic behaviors such as homoclinic bifurcation and chaos under harmonic excitation are investigated. At first, the analytically necessary condition for chaos in the sense of Smale horseshoe is derived based on the Melnikov method.
Shutong Fan +3 more
wiley +1 more source