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Conservative flows with various types of shadowing

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  • Bessa, Mário
  • Ribeiro, Raquel

Abstract

In the present paper we study the C1-robustness of the three properties: average shadowing, asymptotic average shadowing and limit shadowing within two classes of conservative flows: the incompressible and the Hamiltonian ones. We obtain that the first two properties guarantee dominated splitting (or partial hyperbolicity) on the whole manifold, and the third one implies that the flow is Anosov.

Suggested Citation

  • Bessa, Mário & Ribeiro, Raquel, 2015. "Conservative flows with various types of shadowing," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 243-252.
    • Handle: RePEc:eee:chsofr:v:75:y:2015:i:c:p:243-252
    DOI: 10.1016/j.chaos.2015.02.022
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    References listed on IDEAS

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    1. Gu, Rongbao, 2009. "The asymptotic average-shadowing property and transitivity for flows," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2234-2240.
    2. Zamani Bahabadi, Alireza, 2012. "Divergence-free vector fields with average and asymptotic average shadowing property," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1358-1360.
    3. Gu, Rongbao & sheng, Yeqing & Xia, Zhijie, 2005. "The average-shadowing property and transitivity for continuous flows," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 989-995.
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    Cited by:

    1. Garg, Mukta & Das, Ruchi, 2017. "Continuous semi-flows with the almost average shadowing property," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 1-7.

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    1. Garg, Mukta & Das, Ruchi, 2017. "Continuous semi-flows with the almost average shadowing property," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 1-7.
    2. Gu, Rongbao, 2009. "The asymptotic average-shadowing property and transitivity for flows," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2234-2240.
    3. Zamani Bahabadi, Alireza, 2012. "Divergence-free vector fields with average and asymptotic average shadowing property," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1358-1360.

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