Sigma Map Dynamics and Bifurcations

    2017, Volume 22, Number 6, pp.  740–749

    Author(s): Rahman A., Joshi Y., Blackmore D.

    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, invariant sets, homoclinic and heteroclinic orbits, sigma maps, dynamical crises
    Citation: Rahman A., Joshi Y., Blackmore D., Sigma Map Dynamics and Bifurcations, Regular and Chaotic Dynamics, 2017, Volume 22, Number 6, pp. 740–749

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