%0 Journal Article
%T A New Class of Solvable Many-Body Problems
%A Francesco Calogero
%A Ge Yi
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2012
%I National Academy of Science of Ukraine
%X A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velocity-dependent one-body and two-body forces) featuring several arbitrary coupling constants. The corresponding initial-value problems are solved by finding the eigenvalues of a time-dependent N¡ÁN matrix U(t) explicitly defined in terms of the initial positions and velocities of the N particles. Some of these models are asymptotically isochronous, i.e. in the remote future they become completely periodic with a period T independent of the initial data (up to exponentially vanishing corrections). Alternative formulations of these models, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited.
%K integrable dynamical systems
%K solvable dynamical systems
%K solvable Newtonian many-body problems
%K integrable Newtonian many-body problems
%K isochronous dynamical systems
%U http://dx.doi.org/10.3842/SIGMA.2012.066