×

Multiple closed orbits of fixed energy for gravitational potentials. (English) Zbl 0787.34029

The paper gives for any fixed \(h<0\) a lower bound for the number of geometrically distinct closed noncollision trajectories of minimal period of the problem \(\ddot q+V'(q)=0\), \({1\over 2} | \dot q |^ 2+V(q)=h\). Here \(V\) is a potential which behaves like \(V(x)\cong-1/ | x |^ \gamma\) where \(1\leq \gamma<2\). In the proof of the main theorem variational methods are applied. This work is an extension of Ambrosetti’s and the author’s investigations to the case of gravitational potentials.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
70F99 Dynamics of a system of particles, including celestial mechanics
PDFBibTeX XMLCite
Full Text: DOI