Examples of lorenz-like attractors in hénon-like maps

S. V. Gonchenko; A. S. Gonchenko; I. I. Ovsyannikov; D. V. Turaev

doi:10.1051/mmnp/20138504

Examples of lorenz-like attractors in hénon-like maps

S. V. Gonchenko, A. S. Gonchenko, I. I. Ovsyannikov, D. V. Turaev

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

We display a gallery of Lorenz-like attractors that emerge in a class of three-dimensional maps. We review the theory of Lorenz-like attractors for diffeomorphisms (as opposed to flows), define various types of such attractors, and find sufficient conditions for three-dimensional Henon-like maps to possess pseudohyperbolic Lorenz-like attractors. The numerically obtained scenarios of the creation and destruction of these attractors are also presented.

Original language	English
Pages (from-to)	48-70
Number of pages	23
Journal	Mathematical Modelling of Natural Phenomena
Volume	8
Issue number	5
DOIs	https://doi.org/10.1051/mmnp/20138504
State	Published - 14 Oct 2013
Externally published	Yes

Keywords

Bifurcations
Homoclinic orbit
Homoclinic tangency
Normal form
Pseudohyperbolicity
Strange attractor
Three-dimensional maps
Volume hyperbolicity
Wild set

ASJC Scopus subject areas

Modeling and Simulation
Applied Mathematics

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10.1051/mmnp/20138504

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title = "Examples of lorenz-like attractors in h{\'e}non-like maps",

abstract = "We display a gallery of Lorenz-like attractors that emerge in a class of three-dimensional maps. We review the theory of Lorenz-like attractors for diffeomorphisms (as opposed to flows), define various types of such attractors, and find sufficient conditions for three-dimensional Henon-like maps to possess pseudohyperbolic Lorenz-like attractors. The numerically obtained scenarios of the creation and destruction of these attractors are also presented.",

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AU - Gonchenko, S. V.

AU - Gonchenko, A. S.

AU - Ovsyannikov, I. I.

AU - Turaev, D. V.

PY - 2013/10/14

Y1 - 2013/10/14

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AB - We display a gallery of Lorenz-like attractors that emerge in a class of three-dimensional maps. We review the theory of Lorenz-like attractors for diffeomorphisms (as opposed to flows), define various types of such attractors, and find sufficient conditions for three-dimensional Henon-like maps to possess pseudohyperbolic Lorenz-like attractors. The numerically obtained scenarios of the creation and destruction of these attractors are also presented.

KW - Bifurcations

KW - Homoclinic orbit

KW - Homoclinic tangency

KW - Normal form

KW - Pseudohyperbolicity

KW - Strange attractor

KW - Three-dimensional maps

KW - Volume hyperbolicity

KW - Wild set

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IS - 5

ER -

Examples of lorenz-like attractors in hénon-like maps

Abstract

Keywords

ASJC Scopus subject areas

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