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| 1 | Integral expressions of Lyapunov exponents for autonomous ordinary differential systems显示文摘In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space Rd, not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces. | DAI XiongPing Department of Mathematics, Nanjing University, Nanjing 210093, China | 2009 | Science China Mathematics2009，52，1： | 3 |
| 2 | Existence of full-Hausdorff-dimension invariant measures of dynamical systems with dimension metrics显示文摘 | Xiongping Dai | 2005 | Archiv der Mathematik2005，，5： | 1 |
| 3 | On Galvin's theorem for compact Hausdorff right-topological semigroups with dense topological centers显示文摘We generalize an important theorem of Fred Galvin from the Stone-Cˇech compactification βT of any discrete semigroup T to any compact Hausdorff right-topological semigroup with a dense topological center;and then apply it to Ellis' semigroups to prove that a point is distal if and only if it is IP*-recurrent, for any semiflow(T, X) with arbitrary compact Hausdorff phase space X not necessarily metrizable and with arbitrary phase semigroup T not necessarily cancelable. | DAI XiongPing LIANG HaiLan | 2017 | Science China Mathematics2017，60，12： | 1 |
| 4 | Hausdorff Dimensions of Entropy Sets of Dynamical Systems with Positive Entropy显示文摘 | XIONGPING DAI YUNPING JIANG | 2005 | Journal of Statistical Physics2005，，2： | 1 |
| 5 | Erratum to:On Galvin's theorem for compact Hausdorff right-topological semigroups with dense topological centers显示文摘In the third paragraph on p.2421 and in Theorem 1′ of[3]it is wrongly assumed that“the multiplication on a topological semigroup T can be extended to a right continuous multiplication on 0F”;in other words,we wrongly assume that“βT is a compact Hausdorff right-topological semigroup for any topological semigroup T”.So using[3,Theorem 1]we can only obtain the following two theorems in place of[3,Theorem 1′],where X' denotes the limit-point set of a space X and J(E)denotes the set of all idempotents in a compact Hausdorff right?topological semigroup E. | Xiongping Dai Hailan Liang | 2019 | Science China Mathematics2019，62，12： | 0 |
| 6 | Hyperbolicity of C^1 -star invariant sets for C^1 -class dynamical systems显示文摘In this paper, we simply prove, in the framework of Liao, the hyperbolicity of C 1 -star invariant sets of C 1 -class differential systems on a closed manifold of dimension≤ 4, without using the C 1 -connecting lemma and even the ergodic closing lemma. | DAI XiongPing | 2011 | Science China Mathematics2011，54，2： | 0 |
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