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Bifurcations of Periodic Orbits
2008This chapter and Chapter IX use the theory of normal forms developed in Chapter VI. They contain an introduction to generic bifurcation theory and its applications. Bifurcation theory has grown into a vast subject with a large literature; so, this chapter can only present the basics of the theory.
Dan Offin+2 more
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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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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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Brain and other central nervous system tumor statistics, 2021
Ca-A Cancer Journal for Clinicians, 2021Carol Kruchko+2 more
exaly
Cancer statistics for African American/Black People 2022
Ca-A Cancer Journal for Clinicians, 2022Angela N Giaquinto+2 more
exaly
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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