Invariant cones for strange attractors of Lozi, H\'{e}non and Belykh type maps
Dina Grechko, Vladimir Belykh, Nikita Barabash
TL;DR
This paper develops a unified approach using invariant cones to analyze the hyperbolic properties of strange attractors in generalized 2D maps, including Lozi, Hénon, and Belykh types.
Contribution
It introduces a technique for constructing invariant cones to study hyperbolicity in generalized maps, extending the analysis to new modifications of classic attractors.
Findings
Theorems establishing singular hyperbolic attractors for modified maps
A method for creating invariant expanding and contracting cones
Application to Lozi, Hénon, and Belykh map variants
Abstract
We consider strange attractors of two dimensional generalized map with one nonlinearity such that Lozi, H\'{e}non and Belykh maps are particular cases of it. We describe technique of invariant expanding and contracting cones creation for study of hyperbolic properties. Theorems of singular hyperbolic attractors for new modifications of Lozi, H\'{e}non and Belykh-type maps are presented.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Nonlinear Dynamics and Pattern Formation