# Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit

22 Jan 2020 T. Grava A. Maspero G. Mazzuca A. Ponno

We consider the Fermi-Pasta-Ulam-Tsingou (FPUT) chain composed by $N \gg 1$ particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature $\beta^{-1}$. Given a fixed ${1\leq m \ll N}$, we prove that the first $m$ integrals of motion of the periodic Toda chain are adiabatic invariants of FPUT (namely they are approximately constant along the Hamiltonian flow of the FPUT) for times of order $\beta$, for initial data in a set of large measure... (read more)

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