Sigma map dynamics and bifurcations

Aminur Rahman; Yogesh Joshi; Denis Blackmore

doi:10.1134/S1560354717060107

Sigma map dynamics and bifurcations

Aminur Rahman, Yogesh Joshi, Denis Blackmore

Mathematical Sciences

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

10 Scopus citations

Abstract

Some interesting variants of walking droplet based discrete dynamical bifurcations arising from diffeomorphisms are analyzed in detail. A notable feature of these new bifurcations is that, like Smale horseshoes, they can be represented by simple geometric paradigms, which markedly simplify their analysis. The two-dimensional diffeomorphisms that produce these bifurcations are called sigma maps or double sigma maps for reasons that are made manifest in this investigation. Several examples are presented along with their dynamical simulations.

Original language	English (US)
Pages (from-to)	740-749
Number of pages	10
Journal	Regular and Chaotic Dynamics
Volume	22
Issue number	6
DOIs	https://doi.org/10.1134/S1560354717060107
State	Published - Nov 1 2017

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

Keywords

Discrete dynamical systems
bifurcations
chaotic strange attractors
dynamical crises
homoclinic and heteroclinic orbits
invariant sets
sigma maps

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10.1134/S1560354717060107

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abstract = "Some interesting variants of walking droplet based discrete dynamical bifurcations arising from diffeomorphisms are analyzed in detail. A notable feature of these new bifurcations is that, like Smale horseshoes, they can be represented by simple geometric paradigms, which markedly simplify their analysis. The two-dimensional diffeomorphisms that produce these bifurcations are called sigma maps or double sigma maps for reasons that are made manifest in this investigation. Several examples are presented along with their dynamical simulations.",

keywords = "Discrete dynamical systems, bifurcations, chaotic strange attractors, dynamical crises, homoclinic and heteroclinic orbits, invariant sets, sigma maps",

author = "Aminur Rahman and Yogesh Joshi and Denis Blackmore",

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AU - Rahman, Aminur

AU - Joshi, Yogesh

AU - Blackmore, Denis

PY - 2017/11/1

Y1 - 2017/11/1

N2 - Some interesting variants of walking droplet based discrete dynamical bifurcations arising from diffeomorphisms are analyzed in detail. A notable feature of these new bifurcations is that, like Smale horseshoes, they can be represented by simple geometric paradigms, which markedly simplify their analysis. The two-dimensional diffeomorphisms that produce these bifurcations are called sigma maps or double sigma maps for reasons that are made manifest in this investigation. Several examples are presented along with their dynamical simulations.

AB - Some interesting variants of walking droplet based discrete dynamical bifurcations arising from diffeomorphisms are analyzed in detail. A notable feature of these new bifurcations is that, like Smale horseshoes, they can be represented by simple geometric paradigms, which markedly simplify their analysis. The two-dimensional diffeomorphisms that produce these bifurcations are called sigma maps or double sigma maps for reasons that are made manifest in this investigation. Several examples are presented along with their dynamical simulations.

KW - Discrete dynamical systems

KW - bifurcations

KW - chaotic strange attractors

KW - dynamical crises

KW - homoclinic and heteroclinic orbits

KW - invariant sets

KW - sigma maps

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EP - 749

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

IS - 6

ER -

Sigma map dynamics and bifurcations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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