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1994
An intensively used method for finding periodic orbits is Newton’s method and variants thereof. We describe Newton’s method and the Quasi-Newton method later in this section. Newton→s method uses the initialization point y1, marked by the small cross, as its initial point.
Helena E. Nusse +2 more
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An intensively used method for finding periodic orbits is Newton’s method and variants thereof. We describe Newton’s method and the Quasi-Newton method later in this section. Newton→s method uses the initialization point y1, marked by the small cross, as its initial point.
Helena E. Nusse +2 more
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Periodic Orbits Near Homoclinic Orbits
1982It is known that the orbit-structure of a dynamical system near a homoclinic orbit γ is extremely complicated. However, it is only recently that this complicated structure has begun to be understood. It has been shown (under some hypotheses) that, near γ there are infinitely many long periodic orbits. The flow, near γ, admits a singular Poincare map o:
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2020
The moon moves in an ellipse around the earth itself moving in space, in the same common direction from west to east, which is characteristic of all known planetary bodies of the solar system, with the exception of the Uranus satellites, and likewise many comets.
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The moon moves in an ellipse around the earth itself moving in space, in the same common direction from west to east, which is characteristic of all known planetary bodies of the solar system, with the exception of the Uranus satellites, and likewise many comets.
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Determination of periodic orbits
2010Periodic orbits play a very important role in many problems of Celestial Mechanics; for example, their study provides interesting information on spin-orbit and orbital resonances (see [96, 136]). From the dynamical point of view periodic orbits can be used to approximate quasi-periodic trajectories; more precisely, a truncation of the continued ...
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1988
A review is presented of periodic orbits which are of interest to Dynamical Astronomy and their relation to actual systems is given. In particular, we review periodic orbits in planetary systems with two or more planets, in the asteroid system, in stellar systems and in the motion of a star in various types of galaxies.
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A review is presented of periodic orbits which are of interest to Dynamical Astronomy and their relation to actual systems is given. In particular, we review periodic orbits in planetary systems with two or more planets, in the asteroid system, in stellar systems and in the motion of a star in various types of galaxies.
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1971
Suppose f: C → Rn is continuous together with its Frechet derivative and consider the autonomous equation $${\rm{\dot x}}\left( {\rm{t}} \right) = {\rm{f}}\left( {{\rm{x}}_{\rm{t}} } \right)$$ (37.1) .
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Suppose f: C → Rn is continuous together with its Frechet derivative and consider the autonomous equation $${\rm{\dot x}}\left( {\rm{t}} \right) = {\rm{f}}\left( {{\rm{x}}_{\rm{t}} } \right)$$ (37.1) .
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The contour of an orbit and a stable periodic orbit
Astronomy Letters, 2003T. A. Agekyan, N. Yu. Kretser
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