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Super-exponential stability for generic real-analytic elliptic equilibrium points
- Source :
- Advances in Mathematics, Advances in Mathematics, Elsevier, 2020, 366, Advances in Mathematics, 2020, 366, ⟨10.1016/j.aim.2020.107088⟩, HAL
- Publication Year :
- 2020
- Publisher :
- HAL CCSD, 2020.
-
Abstract
- International audience; We consider the dynamics in a neighborhood of an elliptic equilibrium point with a Diophantine frequency of a symplectic real analytic vector field and we prove the following result of effective stability. Generically, both in a topological and measure-theoretical sense, any solution starting sufficiently close to the equilibrium point remains close to it for an interval of time which is doubly exponentially large with respect to the inverse of the distance to the equilibrium point.
- Subjects :
- Equilibrium point
General Mathematics
Diophantine equation
010102 general mathematics
Mathematical analysis
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
Inverse
Interval (mathematics)
01 natural sciences
Stability (probability)
Exponential stability
0103 physical sciences
Vector field
010307 mathematical physics
0101 mathematics
Mathematics
Symplectic geometry
Subjects
Details
- Language :
- English
- ISSN :
- 00018708 and 10902082
- Database :
- OpenAIRE
- Journal :
- Advances in Mathematics, Advances in Mathematics, Elsevier, 2020, 366, Advances in Mathematics, 2020, 366, ⟨10.1016/j.aim.2020.107088⟩, HAL
- Accession number :
- edsair.doi.dedup.....625e53f76df2039b7b45d1adc30ef2aa