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A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems

Robert Krawczyk (2014)

Banach Center Publications

In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system q ̈ + q V ( t , q ) = f ( t ) , where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map q V : × is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.

A theorem for rigid motions in Post-Newtonian celestial mechanics.

J.M. Gambi, P. Zamorano, P. Romero, M.L. García del Pino (2003)

RACSAM

The velocity field distribution for rigid motions in the Born?s sense applied to Post-Newtonian Relativistic Celestial Mechanics is examined together with its compatibility with the Newtonian distribution.

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