Long Quan
Name:Song Shao
Email:songshao@ustc.edu.cn
Welcome to my homepage
some Links
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Ergodic theory and Topological Dynamics:
I. PAPERS AND PREPRINTS：
1. S. Shao and X.D. Ye, Non-wandering sets of the powers of maps of a star, Discrete and Continuous Dynamical Systems, Vol.9, No.5 (2003),1175--1184. pdf
2. W. Huang, S.M. Li, S. Shao and X.D. Ye, Null systems and sequence entropy pairs, Ergodic Theory and Dynamical Systems, Vol. 23, No.5 (2003), 1505--1523. dvi
3. S. Shao and X.D. Ye, F-mixing and weak disjointness, Topology and its Applications, Vol.135, No.1-3, (2004), 231--247. pdf
4. W. Huang, S. Shao and X.D. Ye, Mixing and proximal cell along sequences, Nonlinearity, Vol.17, No.4, (2004), 1245--1260. pdf
5. S. Shao, Dynamical systems with enveloping semigroup containing finitely many idempotents, J. China Univ. Sci. Tech. Vol.35, No.1(2005), 12--24. pdf
6. W. Huang, S. Shao and X.D. Ye, Mixing via sequence entropy, Contemporary Mathematics, Vol 385, (2005), 101--122. pdf
7. S. Shao, Proximity and distality via Furstenberg families, Topology and its Applications, Vol.153, (2006), 2055--2072. pdf
8. J.H. Mai and S. Shao, The Structure of Graph maps without periodic points, Topology and its Applications, Vol 154, (2007), 2714--2728. pdf
9. J.H. Mai and S. Shao, The space of omega-limit sets of a graph map, Fundamenta Mathematicae, Vol.196, No.1 (2007), 91--100. pdf
10. A. Maass and S. Shao, Structure of bounded topological-sequence-entropy minimal systems, Journal of the London Mathematical Society, Vol 76, No.3 (2007), 702--718. pdf
11. S.Shao, X.D. Ye and R.F. Zhang, Sensitivity and regionally proximal relation in minimal systems, Science in China series A, Vol. 51 (6), (2008), 987--994. pdf
12. J.H. Mai and S. Shao, $\overline{R}=R\bigcup \overline{P}$ for graph maps, Journal of Mathematical Analysis and Applications, Volume 350, Issue 1 (2009), 9--11 pdf
13. A. Coronel, A. Maass and S. Shao, Sequence entropy and rigid $\sigma-$algebras, Studia Mathematica, Vol 194 (2009), 207--230. pdf
14. E. Akin, E. Glasner, W. Huang, S. Shao and X.D. Ye, Sufficient conditions under which a transitive system is chaotic, Ergodic Theory and Dynamical Systems, Vol. 30 (2010), 1277--1310. pdf
15. J.H. Mai and S. Shao, Graph maps whose periodic points form a closed set, Journal of Mathematical Analysis and Applications, 371 (2010), 649--654. pdf
16. J.H. Mai and S. Shao, Forcing Relation on Patterns of invariant sets and reductions of interval maps, Transactions of the AMS, 363 (2011), 2517--2549. pdf
17. P.D. Dong, S. Shao and X.D. Ye, Product recurrent properties, disjointness and weak disjointness, Israel J. Math., 188 (2012), 463--507. pdf
18. S. Shao and X.D. Ye, Regionally proximal relation of order d is an equivalence one for minimal systems and a combinatorial consequence, Advances in Mathematics, 231 (2012), 1786--1817. pdf
19. P.D. Dong, S. Donoso, A. Maass, S. Shao and X.D. Ye, Infinite-step nilsystems, independence and complexity, Ergodic Theory and Dynamical Systems, vol.33 (2013),118--143. pdf
20. J.H. Mai and S. Shao, Chaotic expansive homeomorphisms on closed orientable surfaces of positive genus, Communications in Mathematics and Statistics, 3 (2015), 291--314
21. Z. Lian and S. Shao, Relatively weakly mixing models for dynamical systems, Ergodic Theory and Dynamical Systems, 36 (2016), no. 4, 1204–1220. pdf
22. W. Huang, S. Shao and X.D. Ye, Nil Bohr0-sets, Poincare recurrence and generalized polynomials, preprint, 2011. pdf
22'. W. Huang, S. Shao and X.D. Ye, Higher order almost automorphy, recurrence sets and the regionally proximal relation, preprint, 2011. pdf
* The above two paper are put into one paper entitiled "Nil Bohr-sets and almost automorphy of higher order", Memoirs of the AMS, volume 241, Number 1143, 2016. arXiv:1407.1179
23. Z. Lian, S. Shao and X.D. Ye, Weakly mixing, proximal topological models for ergodic systems and applications, Fundamenta Mathematicae,236 (2017), no. 2, 161--185. arXiv:1407.1978
24. S. Donoso and S. Shao, Uniformly rigid models for rigid actions, 236 (2017), no. 1, 13--31. arXiv:1508.03366
25. X.D. Ye and S. Shao, Progress on some recurrence problems in dynamics (dedicated to the 90th birthday of Prof. Zhifen Zhang) (in Chinese), Sci Sin Math, 47(2017), 53—76. pdf
26. W. Huang, S. Shao and X.D. Ye, Strictly ergodic models under face and parallelepiped group actions,Commun. Math. Stat. 5 (2017), no. 1, 93--122. pdf
27. W. Huang, Z. Lian, S. Shao and X.D. Ye, Sequences from zero entropy noncommutative toral automorphisms and Sarnak Conjecture. J. Differential Equations , 263 (2017), no. 1, 779--810. arXiv:1510.06022
28. S. Shao and X.D. Ye, A non-PI minimal system is Li-Yorke sensitive, Proc. Amer. Math. Soc. Vol. 146, No.3, 1105–1112. arXiv:1610.01793 pdf
29. Y. Gutman, W. Huang, S. Shao and X.D. Ye, Almost sure convergence of the multiple ergodic average for certain weakly mixing systems, Acta Math Sinica, 2018 Vol. 34 (1): 79-90. arXiv:1612.02873
30. W. Huang, S. Shao and X.D. Ye, Topological correspondence of multiple ergodic averages of nilpotent group actions, J. Anal. Math. 138 (2019), no. 2, 687–715. arXiv:1604.07113 [math.DS]
31. W. Huang, S. Shao and X.D. Ye, Pointwise convergence of multiple ergodic averages and strictly ergodic models, to appear in Journal d'Analyse Mathematique arXiv:1406.5930
32. W. Huang, S. Shao and X.D. Ye, An answer to Furstenberg' problem on topological disjointness, to appear in Ergodic Theory and Dynamical Systems arXiv:1807.10155
33. F. Cai and S. Shao, Topological characteristic factors along cubes of minimal systems, Discrete Contin. Dyn. Syst. 39 (2019), no. 9, 5301–5317. arXiv:1809.06737
34. E. Glasner, W. Huang, S. Shao and X.D. Ye, Regionally proximal relation of order $d$ along arithmetic progressions and nilsystems, preprint, 2019
35. W. Huang, Z. Lian, S. Shao and X.D. Ye, Minimal systems with finitely many ergodic measures，preprint, 2019.
II. BOOKS
1. Xiangdong Ye, Wen Huang and Song Shao, An Introduction to Topological Dynamics (in Chinese), 2008.3.，China Science Press errata
2. Xiangdong Ye and Song Shao, The Theory of Minimal Flows and Its Applications (in Chinese), in preparation
I. PAPERS AND PREPRINTS：
1. S. Shao and X.D. Ye, Non-wandering sets of the powers of maps of a star, Discrete and Continuous Dynamical Systems, Vol.9, No.5 (2003),1175--1184. pdf
2. W. Huang, S.M. Li, S. Shao and X.D. Ye, Null systems and sequence entropy pairs, Ergodic Theory and Dynamical Systems, Vol. 23, No.5 (2003), 1505--1523. dvi
3. S. Shao and X.D. Ye, F-mixing and weak disjointness, Topology and its Applications, Vol.135, No.1-3, (2004), 231--247. pdf
4. W. Huang, S. Shao and X.D. Ye, Mixing and proximal cell along sequences, Nonlinearity, Vol.17, No.4, (2004), 1245--1260. pdf
5. S. Shao, Dynamical systems with enveloping semigroup containing finitely many idempotents, J. China Univ. Sci. Tech. Vol.35, No.1(2005), 12--24. pdf
6. W. Huang, S. Shao and X.D. Ye, Mixing via sequence entropy, Contemporary Mathematics, Vol 385, (2005), 101--122. pdf
7. S. Shao, Proximity and distality via Furstenberg families, Topology and its Applications, Vol.153, (2006), 2055--2072. pdf
8. J.H. Mai and S. Shao, The Structure of Graph maps without periodic points, Topology and its Applications, Vol 154, (2007), 2714--2728. pdf
9. J.H. Mai and S. Shao, The space of omega-limit sets of a graph map, Fundamenta Mathematicae, Vol.196, No.1 (2007), 91--100. pdf
10. A. Maass and S. Shao, Structure of bounded topological-sequence-entropy minimal systems, Journal of the London Mathematical Society, Vol 76, No.3 (2007), 702--718. pdf
11. S.Shao, X.D. Ye and R.F. Zhang, Sensitivity and regionally proximal relation in minimal systems, Science in China series A, Vol. 51 (6), (2008), 987--994. pdf
12. J.H. Mai and S. Shao, $\overline{R}=R\bigcup \overline{P}$ for graph maps, Journal of Mathematical Analysis and Applications, Volume 350, Issue 1 (2009), 9--11 pdf
13. A. Coronel, A. Maass and S. Shao, Sequence entropy and rigid $\sigma-$algebras, Studia Mathematica, Vol 194 (2009), 207--230. pdf
14. E. Akin, E. Glasner, W. Huang, S. Shao and X.D. Ye, Sufficient conditions under which a transitive system is chaotic, Ergodic Theory and Dynamical Systems, Vol. 30 (2010), 1277--1310. pdf
15. J.H. Mai and S. Shao, Graph maps whose periodic points form a closed set, Journal of Mathematical Analysis and Applications, 371 (2010), 649--654. pdf
16. J.H. Mai and S. Shao, Forcing Relation on Patterns of invariant sets and reductions of interval maps, Transactions of the AMS, 363 (2011), 2517--2549. pdf
17. P.D. Dong, S. Shao and X.D. Ye, Product recurrent properties, disjointness and weak disjointness, Israel J. Math., 188 (2012), 463--507. pdf
18. S. Shao and X.D. Ye, Regionally proximal relation of order d is an equivalence one for minimal systems and a combinatorial consequence, Advances in Mathematics, 231 (2012), 1786--1817. pdf
19. P.D. Dong, S. Donoso, A. Maass, S. Shao and X.D. Ye, Infinite-step nilsystems, independence and complexity, Ergodic Theory and Dynamical Systems, vol.33 (2013),118--143. pdf
20. J.H. Mai and S. Shao, Chaotic expansive homeomorphisms on closed orientable surfaces of positive genus, Communications in Mathematics and Statistics, 3 (2015), 291--314
21. Z. Lian and S. Shao, Relatively weakly mixing models for dynamical systems, Ergodic Theory and Dynamical Systems, 36 (2016), no. 4, 1204–1220. pdf
22. W. Huang, S. Shao and X.D. Ye, Nil Bohr0-sets, Poincare recurrence and generalized polynomials, preprint, 2011. pdf
22'. W. Huang, S. Shao and X.D. Ye, Higher order almost automorphy, recurrence sets and the regionally proximal relation, preprint, 2011. pdf
* The above two paper are put into one paper entitiled "Nil Bohr-sets and almost automorphy of higher order", Memoirs of the AMS, volume 241, Number 1143, 2016. arXiv:1407.1179
23. Z. Lian, S. Shao and X.D. Ye, Weakly mixing, proximal topological models for ergodic systems and applications, Fundamenta Mathematicae,236 (2017), no. 2, 161--185. arXiv:1407.1978
24. S. Donoso and S. Shao, Uniformly rigid models for rigid actions, 236 (2017), no. 1, 13--31. arXiv:1508.03366
25. X.D. Ye and S. Shao, Progress on some recurrence problems in dynamics (dedicated to the 90th birthday of Prof. Zhifen Zhang) (in Chinese), Sci Sin Math, 47(2017), 53—76. pdf
26. W. Huang, S. Shao and X.D. Ye, Strictly ergodic models under face and parallelepiped group actions,Commun. Math. Stat. 5 (2017), no. 1, 93--122. pdf
27. W. Huang, Z. Lian, S. Shao and X.D. Ye, Sequences from zero entropy noncommutative toral automorphisms and Sarnak Conjecture. J. Differential Equations , 263 (2017), no. 1, 779--810. arXiv:1510.06022
28. S. Shao and X.D. Ye, A non-PI minimal system is Li-Yorke sensitive, Proc. Amer. Math. Soc. Vol. 146, No.3, 1105–1112. arXiv:1610.01793 pdf
29. Y. Gutman, W. Huang, S. Shao and X.D. Ye, Almost sure convergence of the multiple ergodic average for certain weakly mixing systems, Acta Math Sinica, 2018 Vol. 34 (1): 79-90. arXiv:1612.02873
30. W. Huang, S. Shao and X.D. Ye, Topological correspondence of multiple ergodic averages of nilpotent group actions, J. Anal. Math. 138 (2019), no. 2, 687–715. arXiv:1604.07113 [math.DS]
31. W. Huang, S. Shao and X.D. Ye, Pointwise convergence of multiple ergodic averages and strictly ergodic models, to appear in Journal d'Analyse Mathematique arXiv:1406.5930
32. W. Huang, S. Shao and X.D. Ye, An answer to Furstenberg' problem on topological disjointness, to appear in Ergodic Theory and Dynamical Systems arXiv:1807.10155
33. F. Cai and S. Shao, Topological characteristic factors along cubes of minimal systems, Discrete Contin. Dyn. Syst. 39 (2019), no. 9, 5301–5317. arXiv:1809.06737
34. E. Glasner, W. Huang, S. Shao and X.D. Ye, Regionally proximal relation of order $d$ along arithmetic progressions and nilsystems, preprint, 2019
35. W. Huang, Z. Lian, S. Shao and X.D. Ye, Minimal systems with finitely many ergodic measures，preprint, 2019.
II. BOOKS
1. Xiangdong Ye, Wen Huang and Song Shao, An Introduction to Topological Dynamics (in Chinese), 2008.3.，China Science Press errata
2. Xiangdong Ye and Song Shao, The Theory of Minimal Flows and Its Applications (in Chinese), in preparation
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