On the algebraic properties of exponentially stable integrable hamiltonian systems

Santiago Barbieri

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arXiv · 2011.09731

On the algebraic properties of exponentially stable integrable hamiltonian systems

Santiago Barbieri

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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.

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Santiago Barbieri. 2020-11-19. On the algebraic properties of exponentially stable integrable hamiltonian systems. https://arxiv.org/abs/2011.09731

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