Puiseux series polynomial dynamics and iteration of complex cubic polynomials
We let be the completion of the field of formal Puiseux series and study polynomials with coefficients in as dynamical systems. We give a complete description of the dynamical and parameter space of cubic polynomials in . We show that cubic polynomial dynamics over and are intimately related. More precisely, we establish that some elements of naturally correspond to the Fourier series of analytic almost periodic functions (in the sense of Bohr) which parametrize (near infinity) the quasiconformal...