DERIVING CHAOTIC DYNAMICAL SYSTEMS FROM ENERGY FUNCTIONALS
Paul Bracken, Paweł Góra, Abraham Boyarsky · Stochastics and Dynamics · 2001
Simple one-dimensional chaotic dynamical systems are derived by optimizing energy functionals. The Euler–Lagrange equation yields a nonlinear second-order differential equation whose solution yields a 2–1 map which admits an absolutely continuous invariant measure. The solutions of the differential equation are studied.