Geodesic
Distributional chaos for flows
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 475-480
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Schweizer and Smítal introduced the distributional chaos for continuous maps of the interval in B. Schweizer, J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Amer. Math. Soc. 344 (1994), 737–854. In this paper, we discuss the distributional chaos DC1–DC3 for flows on compact metric spaces. We prove that both the distributional chaos DC1 and DC2 of a flow are equivalent to the time-1 maps and so some properties of DC1 and DC2 for discrete systems also hold for flows. However, we prove that DC2 and DC3 are not invariants of equivalent flows although DC2 is a topological conjugacy invariant in discrete case.
Schweizer and Smítal introduced the distributional chaos for continuous maps of the interval in B. Schweizer, J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Amer. Math. Soc. 344 (1994), 737–854. In this paper, we discuss the distributional chaos DC1–DC3 for flows on compact metric spaces. We prove that both the distributional chaos DC1 and DC2 of a flow are equivalent to the time-1 maps and so some properties of DC1 and DC2 for discrete systems also hold for flows. However, we prove that DC2 and DC3 are not invariants of equivalent flows although DC2 is a topological conjugacy invariant in discrete case.
DOI : 10.1007/s10587-013-0031-3
Classification : 37B05, 37B99, 37E25
Keywords: distributional chaos; flow; invariant 
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Zhou, Yunhua. Distributional chaos for flows. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 475-480. doi: 10.1007/s10587-013-0031-3

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