Periodic solutions to a forced Kepler problem in the plane
| Autor: | Duccio Papini, Walter Dambrosio, Alberto Boscaggin |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Periodic solutions
Applied Mathematics General Mathematics 010102 general mathematics Collisions Kepler problem Variational methods Dynamical Systems (math.DS) 16. Peace & justice 01 natural sciences 010101 applied mathematics Combinatorics symbols.namesake FOS: Mathematics symbols Nabla symbol 0101 mathematics Mathematics - Dynamical Systems Mathematics |
| Popis: | Given a smooth function U ( t , x ) U(t,x) , T T -periodic in the first variable and satisfying U ( t , x ) = O ( | x | α ) U(t,x) = \mathcal {O}(\vert x \vert ^{\alpha }) for some α ∈ ( 0 , 2 ) \alpha \in (0,2) as | x | → ∞ \vert x \vert \to \infty , we prove that the forced Kepler problem x ¨ = − x | x | 3 + ∇ x U ( t , x ) , x ∈ R 2 , \begin{equation*} \ddot x = - \dfrac {x}{|x|^3} + \nabla _x U(t,x),\qquad x\in \mathbb {R}^2, \end{equation*} has a generalized T T -periodic solution, according to the definition given in the paper by A. Boscaggin, R. Ortega, and L. Zhao [Trans. Amer. Math. Soc. 372 (2019), 677–703]. The proof relies on variational arguments. |
| Databáze: | OpenAIRE |
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