Abstract
The topological r-entropy and measure theoretic r-entropy of a flow are studied. For a flow (X,φ), it is shown that topological (measure theoretic) r-entropy is equal to the topological (measure theoretic) entropy of the time one map φ1 as r decreases to zero. The Brin—Katok’s entropy formula for r-entropy is also established.
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The authors were Supported by NNSF of China (Grant Nos. 12071222, 11971236), the first author was also Supported by NNSF of China (Grant No. 12101340)
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Ji, Y., Wang, Y.P. Topological r-entropy and Measure Theoretic r-entropy of Flows. Acta. Math. Sin.-English Ser. 38, 761–769 (2022). https://doi.org/10.1007/s10114-022-0573-0
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DOI: https://doi.org/10.1007/s10114-022-0573-0