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pro vyhledávání: '"Capiński, Maciej J."'
We consider the Earth-Moon planar circular restricted three body problem and present a proof of the existence orbits, which approach arbitrarily close to one of the primary masses, and at the same time after each approach they move away from the mass
Externí odkaz:
http://arxiv.org/abs/2401.12386
The Restricted Planar Circular 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies, called the primaries, which perform circular orbits coplanar with that of the massless body. In rota
Externí odkaz:
http://arxiv.org/abs/2312.13138
A diffeomorphism exhibits a blender if it has an invariant hyperbolic set with the $C^1$-robust property that its stable or unstable manifold behaves as a higher-dimensional set than is expected from the underlying hyperbolic splitting. We present a
Externí odkaz:
http://arxiv.org/abs/2212.04861
Consider analytic generic unfoldings of the three dimensional conservative Hopf-Zero singularity. Under open conditions on the parameters determining the singularity, the unfolding possesses two saddle-foci when the unfolding parameter is small enoug
Externí odkaz:
http://arxiv.org/abs/2206.13840
This paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a-posteriori framework for computer assisted existence proofs. Our framework is applied to the study colli
Externí odkaz:
http://arxiv.org/abs/2205.03922
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 obtain the exi
Externí odkaz:
http://arxiv.org/abs/2106.06254
Autor:
Capiński, Maciej J., Wodka, Natalia
We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. We treat the elliptic problem as a perturbation of the circular problem, where the perturbation parameter is the eccentricity of the primaries. Th
Externí odkaz:
http://arxiv.org/abs/2105.07204
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 approach.
Externí odkaz:
http://arxiv.org/abs/2102.06436
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Publikováno v:
In Journal of Differential Equations 5 September 2023 366:132-191