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The three-body problem is arguably the oldest open question in astrophysics, and has resisted a general analytic solution for centuries. Various implementations of perturbation theory provide solutions in portions of parameter space, but…

Astrophysics of Galaxies · Physics 2020-03-18 Nicholas C. Stone , Nathan W. C. Leigh

In this comprehensive and detailed study, vacancy-mediated self-diffusion of A- and B-elements in 'triple-defect' B2-ordered ASB(1-S) binaries is simulated by means of a kinetic Monte Carlo (KMC) algorithm involving atomic jumps to…

Materials Science · Physics 2019-10-16 Jan Betlej , Piotr Sowa , Rafal Kozubski , Graeme E. Murch , Irina V. Belova

We construct a Nekhoroshev-like result of stability with sharp constants for the planar three body problem, both in the planetary and in the restricted circular case, by using the periodic averaging technique. Our constructions can be…

Mathematical Physics · Physics 2018-10-16 Santiago Barbieri , Laurent Niederman

We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor-Hoenselaers-Perj\'es procedure, we perform an expansion in the mass potential of a static…

General Relativity and Quantum Cosmology · Physics 2017-01-05 F. L. Dubeibe , F. D. Lora-Clavijo , Guillermo A. González

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…

Dynamical Systems · Mathematics 2026-02-24 Joshua Fitzgerald , Shane Ross

Normally hyperbolic invariant manifolds theory provides an efficient tool for proving diffusion in dynamical systems. In this paper we develop a methodology for computer assisted proofs of diffusion in a-priori chaotic systems based on this…

Dynamical Systems · Mathematics 2022-01-05 Maciej J. Capinski , Jorge Gonzalez , Jean-Pierre Marco , J. D. Mireles James

This paper investigates the restricted circular planar three-body problem. We prove that for every negative Jacobi constant of sufficiently large magnitude, the surface of unperturbed parabolic solutions breaks to induce homoclinic tangle…

Classical Analysis and ODEs · Mathematics 2025-05-13 Rongchang Liu , Qiudong Wang

Consider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodies (the primaries) moving on circular orbits. By considering…

Mathematical Physics · Physics 2025-12-24 Marcel Guardia , José Lamas , Tere M-Seara

Understanding the deep connection of microscopic dynamics and statistical regularity yields insights into the foundation of statistical mechanics. In this work, based on the classical three-body system under the Lennard-Jones potential upon…

Statistical Mechanics · Physics 2023-12-11 Zhenwei Yao

We investigate a single particle on a 3-dimensional, cubic lattice with a random on-site potential (3D Anderson model). We concretely address the question whether or not the dynamics of the particle is in full accord with the diffusion…

Statistical Mechanics · Physics 2010-05-05 Robin Steinigeweg , Jochen Gemmer

We describe a mechanism for transport of energy in a mechanical system consisting of a pendulum and a rotator subject to a random perturbation. The perturbation that we consider is the product of a Hamiltonian vector field and a scalar,…

Dynamical Systems · Mathematics 2024-09-06 Anna Maria Cherubini , Marian Gidea

We set up a methodology for computer assisted proofs of the existence and the KAM stability of an arbitrary periodic orbit for Hamiltonian systems. We give two examples of application for systems with 2 and 3 degrees of freedom. The first…

Dynamical Systems · Mathematics 2011-05-18 Tomasz Kapela , Carles Simó

We introduce quantum circuits in two and three spatial dimensions which are classically simulable, despite producing a high degree of operator entanglement. We provide a partial characterization of these "automaton" quantum circuits, and…

Statistical Mechanics · Physics 2019-12-10 Jason Iaconis , Sagar Vijay , Rahul Nandkishore

Diffusion has been widely used to describe a random walk of particles or waves, and it requires only one parameter -- the diffusion constant. For waves, however, diffusion is an approximation that disregards the possibility of interference.…

Optics · Physics 2014-01-23 Alexey G. Yamilov , Raktim Sarma , Brandon Redding , Ben Payne , Heeso Noh , Hui Cao

We present results of numerical calculations showing a three-body orbit's period's $T$ dependence on its topology. This dependence is a simple linear one, when expressed in terms of appropriate variables, suggesting an exact mathematical…

Classical Physics · Physics 2015-07-30 V. Dmitrašinović , Milovan Šuvakov

We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating…

Dynamical Systems · Mathematics 2025-10-28 Alessandra Celletti , Christoph Lhotka , Giuseppe Pucacco

Consider the Restricted Planar Circular 3 Body Problem with both realistic mass ratio and Jacobi constant for the Sun-Jupiter pair. We prove the existence of all possible combinations of past and future final motions. In particular, we…

Dynamical Systems · Mathematics 2021-06-14 Maciej J. Capiński , Marcel Guardia , Pau Martín , Tere Seara , Piotr Zgliczyński

The case of the planar circular restricted three-body problem is used as a test field in order to determine the character of the orbits of a small body which moves under the gravitational influence of the two heavy primary bodies. We…

Space Physics · Physics 2017-09-28 Euaggelos E. Zotos

We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular)…

Statistical Mechanics · Physics 2007-05-23 Qiuping A. Wang , Wei Li

This paper investigates the secular motion of a massless asteroid within the framework of the double-averaged elliptic restricted three-body problem. By employing Poincar\'e variables, we analyze the stability properties of asteroid orbits…

Earth and Planetary Astrophysics · Physics 2024-09-10 Yan Luo , Kaicheng Sheng