Continuum-wise expansiveness for non-conservative or conservative systems |
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| Affiliation: | 1. School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500, People’s Republic of China;2. Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, People’s Republic of China |
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| Abstract: | In this paper, we show that a non-conservative vector field is robustly continuum-wise expansive if and only if it satisfies both Axiom A and the quasi-transversality condition. Moreover, a conservative vector field (divergence-free vector field, Hamiltonian system) is robustly continuum-wise expansive if and only if it is Anosov. |
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