On Examples of Pseudohyperbolic Attractors in Flows and Maps

In this paper we give some known examples of pseudohyperbolic attractors of systems of differential equations and diffeomorphisms and also describe our numerical method for the verification of strange attractors on pseudohyperbolicity. By means of this method we give numerical evidence of the pseudohyperbolicity of the Lorenz attractor in the Lyubimov–Zaks model, the wild spiral attractor of Turaev and Shilnikov type in a four-dimensional Lorenz system, various discrete attractors of Lorenz type in three-dimensional Hénon maps, and the figure-eight attractor in the nonholonomic model of Chaplygin top.