On the Lyapunov exponents of the asteroidal motion subject to resonances and encounters
Ivan I. Shevchenko (2006)
- Published
- Aug 1, 2006
- Journal
- Proceedings of the International Astronomical Union · Vol. 2 · No. S236
- DOI
- 10.1017/S174392130700302X
At a GlanceAI
Analytic Lyapunov-time estimates for asteroids near mean-motion resonances and encounters using a unified separatrix-map framework.
SummaryAI
Predictability of asteroid orbits is set by the Lyapunov time, but it is often obtained only by expensive numerical integrations. Shevchenko presents an analytical method to estimate the maximum Lyapunov exponent for two key chaos sources relevant to Lidov–Kozai contexts: motion near ordinary/three-body mean-motion resonances and motion on highly eccentric orbits undergoing moderately close planetary encounters. A single separatrix-map theory framework is used to treat both settings and the resulting Lyapunov-time estimates are checked against previously published numerical values. This offers a practical way to connect resonant/encounter-driven chaos to forecast horizons in asteroid dynamics.
Method SnapshotAI
Analytical estimation of maximum Lyapunov exponents via general separatrix-map theory, with comparison to published numerical integrations.
BackgroundAI
Celestial mechanics of mean-motion resonances (including three-body), chaos/Lyapunov exponents, and basic separatrix-map concepts (relevant to Lidov–Kozai–driven eccentricity changes).