On the algebraic properties of exponentially stable integrable hamiltonian systems

2020/11/19 by Barbieri, Santiago
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.09731

Abstract

Steepness is a geometric property which, together with complex-analyticity, is needed in order to insure stability of a near-integrable hamiltonian system over exponentially long times. Following a strategy developed by Nekhoro-shev, we construct sufficient algebraic conditions for steepness for a given function that involve algebraic equations on its derivatives up to order five. The underlying analysis suggests some interesting considerations on the gener-icity of steepness and represents a first step towards the construction of sufficient conditions for steepness involving the derivatives of the studied function up to an arbitrary order.

Related

• Semi-algebraic Geometry and generic Hamiltonian stability
• The Steep Nekhoroshev's Theorem
• Flexibility and analytic smoothing in averaging theory
• An example of instability in high-dimensional Hamiltonian systems
• Nekhoroshev estimates for finitely differentiable quasi-convex Hamiltonians