Kolmogorov condition near hyperbolic singularities of integrable Hamiltonian systems

TL;DR

This paper demonstrates that integrable Hamiltonian systems with nondegenerate hyperbolic singularities satisfy the Kolmogorov nondegeneracy condition near those singularities, under mild additional assumptions.

Contribution

It establishes a link between hyperbolic singularities and Kolmogorov nondegeneracy in integrable Hamiltonian systems, extending understanding of their local behavior.

Findings

Hyperbolic singularities imply Kolmogorov nondegeneracy near them

The result holds under mild additional conditions

Applicable to singularities containing fixed points

Abstract

In this paper we show that, if an integrable Hamiltonian system admits a nondegenerate hyperbolic singularity then it will satisfy the Kolmogorov condegeneracy condition near that singularity (under a mild additional condition, which is trivial if the singularity contains a fixed point)