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 CU;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 CU;1, i.e. it is not too complex. © Springer Science+Business Media B.V. 2011.