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The average-shadowing property and transitivity for continuous flows
Institution:1. Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, PR China;2. Department of Mathematics, Anhui University, Hefei 230039, PR China;1. Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China;2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China;3. Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, Academician Glushkov prospectus 4-b, 03127 Kyiv, Ukraine;4. Institute of Mathematics, NASU, Tereshchenkivs''ka 3, 01601 Kyiv, Ukraine;5. School of Mathematical Sciences and LMNS, Fudan University and Shanghai Center for Mathematical Sciences, Shanghai 200433, China;1. School of the Environment, Jiangsu University, Zhenjiang 212013, PR China;2. School of Biology and Chemical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212018, PR China;3. School of Chemistry and Chemical Engineering, Jiangsu University, Zhenjiang 212013, PR China
Abstract:We prove that a continuous flow with the average-shadowing property is chain transitive and a Lyapunov stable continuous flow with the average-shadowing property is a minimal flow.
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