Titlebook: Kepler Problem in the Presence of Dark Energy, and the Cosmic Local Flow; Alexander Silbergleit,Arthur Chernin Book 2019 The Author(s), un

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Orbital (Planar) Motions: Exact Solution and Its Analysis,lem, infinite motions grossly dominate the finite ones. We present and discuss all elementary function solutions existing for special values of . and ., such as circular and spiral orbits. All other cases lead to solutions in terms of Legendre elliptical integrals.

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Radial Motions: Exact Solution and Its Analysis,the Friedmann relativistic solution for expanding universe filled with no-pressure matter and DE. Other cases are reduced to a combination of the standard Legendre elliptical integrals and elementary functions, with derivations partly in Appendix?A.

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Introduction,We give a brief history of dark energy, including recent work on its role in the dynamics of local galactic flows, as motivation for the book contents. Its structure is outlined.

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All Motions: Summary. Locality and Stability of Finite Motions,We summarize the properties of all found solutions, and show that finite motions are essentially localized, predominantly within the no-gravity sphere. We then discuss their stability and show that, with the exception of generic periodic and aperiodic motions described by elliptic integrals, finite motions are structurally unstable.

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