Nekhoroshev

Nekhoroshev is a Russian surname. The most notable bearer is Nikolai Nikolaevich Nekhoroshev, a Russian mathematician known for his work in dynamical systems and mathematical physics. He is best remembered for Nekhoroshev's theorem, a foundational result in the theory of Hamiltonian dynamics.

Nekhoroshev's theorem addresses the long-term stability of nearly integrable Hamiltonian systems. In this framework, the Hamiltonian is written as H(I, θ) = h(I) + ε f(I, θ), where I denotes action variables and θ denotes angle variables, and ε is a small perturbation parameter. Under certain regularity conditions on the unperturbed part h(I)—notably steepness or quasi-convexity—and for sufficiently small ε, the theorem guarantees that the actions I remain close to their initial values for times that grow exponentially as ε decreases. This provides a quantitative form of stability for nearly integrable systems beyond what is ensured by standard perturbation theory, and it complements results from Kolmogorov–Arnold–Moser (KAM) theory.

The theorem has had significant influence in celestial mechanics, plasma physics, and the broader study of Hamiltonian dynamics, where understanding the persistence of quasi-periodic motions under perturbations is essential. Nekhoroshev's surname is of Russian origin and is transliterated in several ways in scholarly literature. The name is primarily associated with the stability theorem in mathematics and its applications.