Geometric Lorenz Attractor and Orbital Shadowing Property

Abstract

Abstract. Komuro [3] proved that geometric Lorentz attractor does not satisfy the shadowing property. In this paper we study the condition under which geometric Lorenz attractor has the orbital shadowing property that is weaker than the shadowing property.Geometric Lorenz attractor is a dynamical system constructed by Guckenheimer in order to analyse Lorenz system of equations which is related to fluid conviction. Numerical observation indicates that all solutions of the Lorenz system pass transversely through a square which will be denoted by Σ, and so a two-dimensional invertible Poincaré map F can be defined on Σ as in Figure 1 (for more details, see [1]).