Results 11 to 20 of about 1,457 (83)

Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics [PDF]

, 2000
In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem.
Koon, Wang Sang, Lo, Martin W., Marsden, Jerrold E., Ross, Shane D.   +3 more
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Motion of vortices implies chaos in Bohmian mechanics [PDF]

, 2005
Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they are at rest ...
, Bialynicki-Birula I., Boffeta G., Bohm D., D. A Wisniacki, Dirac P. A. M., E. R Pujals, Guckenheimer J., Holland P. R., Palis J., Pujals E., Wisniacki D. A., Wu H., Zehnder E.   +13 more
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Mixing-like properties for some generic and robust dynamics [PDF]

, 2014
We show that the set of Bernoulli measures of an isolated topologically mixing homoclinic class of a generic diffeomorphism is a dense subset of the set of invariant measures supported on the class.
Arbieto, Alexander, Catalan, Thiago, Santiago, Bruno   +2 more
core   +1 more source

Homoclinic Orbits In Slowly Varying Oscillators [PDF]

, 1987
We obtain existence and bifurcation theorems for homoclinic orbits in three-dimensional flows that are perturbations of families of planar Hamiltonian systems. The perturbations may or may not depend explicitly on time.
Holmes, Philip, Wiggins, Stephen
core   +1 more source

Homoclinic crossing in open systems: Chaos in periodically perturbed monopole plus quadrupolelike potentials [PDF]

, 2002
The Melnikov method is applied to periodically perturbed open systems modeled by an inverse--square--law attraction center plus a quadrupolelike term. A compactification approach that regularizes periodic orbits at infinity is introduced.
A. E. Motter, A. Kenfack, A.M. Ozorio de Almeida, C. Chicone, D. Hennig, E. Ott, F.Kh. Abdullaev, G.D. Birkhoff, H. Bai-lin, H. Dankowicz, H. Poincaré, I.S. Gradshteyn, I.W. Stewart, J. Casasayas, J. Guckenheimer, J. Koiller, J. Moser, O.E. Gerhard, O.E. Gerhard, P. S. Letelier, P.S. Letelier, P.S. Letelier, R. McGehee, R. Moeckel, S. Chandrasekhar, S. Smale, T. Ahn, V.I. Arnold, V.K.Melnikov, X. Yao, Z. Xia   +30 more
core   +2 more sources

Transition Tori in the Planar Restricted Elliptic Three Body Problem

, 2011
We consider the elliptic three body problem as a perturbation of the circular problem. We show that for sufficiently small eccentricities of the elliptic problem, and for energies sufficiently close to the energy of the libration point L2, a Cantor set ...
Capinski, Maciej J., Zgliczynski, Piotr
core   +1 more source

Intersections of Lagrangian submanifolds and the Mel'nikov 1-form

, 2006
We make explicit the geometric content of Mel'nikov's method for detecting heteroclinic points between transversally hyperbolic periodic orbits.
Abraham, Arnol’d, Chierchia, Colin de Verdière, Delshams, Delshams, Eliasson, Fenichel, Holmes, Lochak, Mel’nikov, Nicolas Roy, Weinstein, Wiggins, Zung   +14 more
core   +1 more source

The Effects of Fluctuating Carrying Capacity on the Dynamics of a Holling‐Type III Predator–Prey Model

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study investigates the complex dynamics of a predator–prey system governed by the classical Lotka–Volterra model incorporating a Holling‐type III. To capture environmental variability, the prey’s carrying capacity is modeled as a periodic function, introducing a time‐dependent forcing into the system.
Ali Sarrah, Faizah J. Alanazi, Mehmet Yavuz, Sayed Saber, Mengxin Chen   +4 more
wiley   +1 more source

Uniqueness of SRB measures for transitive diffeomorphisms on surfaces

, 2010
We give a description of ergodic components of SRB measures in terms of ergodic homoclinic classes associated to hyperbolic periodic points. For transitive surface diffeomorphisms, we prove that there exists at most one SRB measure.Comment: 18 pages, 4 ...
Hertz, F. Rodriguez, Hertz, M. A. Rodriguez, Tahzibi, A., Ures, R.   +3 more
core   +1 more source

Homoclinic chaos in the dynamics of a general Bianchi IX model [PDF]

, 2002
The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the
A. E. Motter, A. Latifi, A. M. Ozorio de Almeida, B. K. Berger, B. K. Berger, B. K. Berger, C. W. Misner, D. F. Chernoff, E. V. Tonini, G. A. Monerat, G. Contopoulos, G. Francisco, H. P. de Oliveira, H. P. de Oliveira, H. V. McIntosh, I. Damião Soares, J. D. Barrow, J. Koiller, N. J. Cornish, N. J. Cornish, N. J. Cornish, R. Barguine, S. Blehar, S. E. Rugh, V. A. Belinskii, V. A. Belinskii   +25 more
core   +2 more sources