An Exactly Solvable Chaotic Differential Equation
نویسندگان
چکیده
We show that continuous-time chaos can be defined using linear dynamics and represented by an exact analytic solution. A driven linear differential equation is used to define a low-dimensional chaotic set of continuous-time waveforms. A nonlinear differential equation is derived for which these waveforms are exact analytic solutions. This nonlinear system describes a chaotic semiflow with a return map that is a chaotic shift map. An extension to the nonlinear differential equation yields an invertible flow with an exact analytic solution and a return map that is a baker’s map. Significantly, these exactly solvable nonlinear systems provide the first examples of which we are aware of chaotic ordinary differential equations possessing an exact symbolic dynamics.
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