An index theory for asymptotic motions under singular potentials
| Autor: | Xijun Hu, Susanna Terracini, Vivina Barutello, Alessandro Portaluri |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Index (economics) Index theory General Mathematics Structure (category theory) Collapse (topology) Dynamical Systems (math.DS) 01 natural sciences Colliding trajectories Lagrangian system 0103 physical sciences FOS: Mathematics Mathematics - Dynamical Systems 0101 mathematics Homothetic orbits Maslov index Parabolic motions Spectral flow Mathematics Spectral index 010102 general mathematics Mathematical analysis 70F10 70F15 70F16 37B30 58J30 53D12 70G75 Compact space Line (geometry) 010307 mathematical physics |
| Zdroj: | Advances in Mathematics. 370:107230 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2020.107230 |
| Popis: | We develop an index theory for parabolic and collision solutions to the classical n-body problem and we prove sufficient conditions for the finiteness of the spectral index valid in a large class of trajectories ending with a total collapse or expanding with vanishing limiting velocities. Both problems suffer from a lack of compactness and can be brought in a similar form of a Lagrangian System on the half time line by a regularising change of coordinates which preserve the Lagrangian structure. We then introduce a Maslov-type index which is suitable to capture the asymptotic nature of these trajectories as half-clinic orbits: by taking into account the underlying Hamiltonian structure we define the appropriate notion of geometric index for this class of solutions and we develop the relative index theory. Comment: 35 pages, 2 figures. v2: changes are mostly in Section 3. Section 5 deleted and reference list updated |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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