From attractor to chaotic saddle: a tale of transverse instability

@article{Ashwin1996FromAT,
  title={From attractor to chaotic saddle: a tale of transverse instability},
  author={P. Ashwin and J. Buescu and I. Stewart},
  journal={Nonlinearity},
  year={1996},
  volume={9},
  pages={703-737}
}
  • P. Ashwin, J. Buescu, I. Stewart
  • Published 1996
  • Mathematics
  • Nonlinearity
  • Suppose that a dynamical system possesses an invariant submanifold, and the restriction of the system to this submanifold has a chaotic attractor A. Under which conditions is A an attractor for the original system, and in what sense? We characterize the transverse dynamics near A in terms of the normal Liapunov spectrum of A. In particular, we emphasize the role of invariant measures on A. Our results identify the points at which A: (1) ceases to be asymptotically stable, possibly developing a… CONTINUE READING
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    References

    SHOWING 1-10 OF 66 REFERENCES
    SYMMETRY BREAKING BIFURCATIONS OF CHAOTIC ATTRACTORS
    • 20
    • Highly Influential
    • PDF
    The structure of symmetric attractors
    • 73
    • PDF
    Blowout bifurcations: the occurrence of riddled basins and on-off intermittency
    • 364
    • Highly Influential
    Abundance of strange attractors
    • 320
    Symmetry-increasing bifurcation of chaotic attractors
    • 144
    • PDF