Fermat’s last theorem and chaoticity

Abstract

Proving that a dynamical system is chaotic is a central problem in chaos theory (Hirsch in Chaos, fractals and dynamics, 1985]. In this note we apply the computational method developed in (Calude and Calude in Complex Syst 18:267---285, 2009; Calude and Calude in Complex Syst 18:387---401, 2010; Calude et al in J Multi Valued Log Soft Comput 12:285---307, 2006) to show that Fermat's last theorem is in the lowest complexity class $${{\mathfrak C}_{U,1}}$$ . Using this result we prove the existence of a two-dimensional Hamiltonian system for which the proof that the system has a Smale horseshoe is in the class $${{\mathfrak C}_{U,1}}$$ , i.e. it is not too complex.