On discrete pseudohyperbolic attractors of Lorenz type

TL;DR

This paper investigates the properties and emergence scenarios of discrete Lorenz-like attractors in three-dimensional maps, revealing new types of pseudohyperbolic attractors and their dynamical behaviors.

Contribution

It introduces new phenomenological scenarios for the appearance of discrete Lorenz-like attractors and demonstrates their existence in generalized Hénon maps.

Findings

Identification of scenarios leading to period-2 Lorenz-like attractors

Discovery of crises leading to new pseudohyperbolic attractors

Examples of attractors in three-dimensional generalized Hénon maps

Abstract

We study geometrical and dynamical properties of the so-called discrete Lorenz-like attractors, that can be observed in three-dimensional diffeomorphisms. We propose new phenomenological scenarios of their appearance in one parameter families of such maps. We pay especially our attention to such a scenario that can lead to period-2 Lorenz-like attractors. These attractors have very interesting dynamical properties and we show that their crises can lead, in turn, to the emergence of pseudohyperbolic discrete Lorenz shape attractors of new types. We also show examples of all these attractors in three-dimensional generalized H\'enon maps.