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Talk:Belykh map - Scholarpedia

Talk:Belykh map

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    It would be helpful if in fig.4 the Poincaré section could be shown. Another comment is that at the beginning of the 3-d embedding the motivation for doing this should be given

    Author Belykh : Response to Referee B

    We are grateful to the referee for the constructive suggestions.

    Following the suggestions we have added three additional figures (Figs. 5-7) illustrating the embedding and the choice of the cross-section. As a motivation for the embedding, we have included a new paragraph:

    "The Belykh map and its planar attractor can be embedded into the phase space of a system of ordinary differential equations (ODEs). The motivation for finding possible flow embeddings of planar discrete-time chaotic attractors is two-fold. First, it gives specific examples of ODE systems, possessing strange attractors with rigorously proven chaotic properties. While planar attractors of discrete-time maps such as, for example, the baker's map, the Lozi map, and the Belykh map have been analytically shown to exhibit quasi-hyperbolic strange attractors, rigorous proofs of chaoticity in ODE systems are rare and often require computer assistance. In light of this, finding a systematic way of planar attractors embedding has its own value for the theory of dynamical systems. Second, these embeddings are an excellent way of visualizing discrete-time attractors and creating graphically appealing images."

    Thank you for your help.

    Igor Belykh.

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