A robustly transitive diffeomorphism of Kan's type
Pages: 867  888,
Issue 2,
February
2018
doi:10.3934/dcds.2018037 Abstract
References
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Cheng Cheng  School of Mathematical Sciences, Peking University, Beijing 100871, China (email)
Shaobo Gan  School of Mathematical Sciences, Peking University, Beijing 100871, China (email)
Yi Shi  School of Mathematical Sciences, Peking University, Beijing 100871, China (email)
1 
F. Abdenur and S. Crovisier, Transitivity and topological mixing for $C^1$ diffeomorphisms, in Essays in Mathematics and Its Applications, Springer, Heidelberg, 2012, 116. 

2 
J. F. Alves, C. Bonatti and M. Viana, SRB measures for partially hyperbolic diffeomorphisms whose central direction is mostly expanding, Invent. Math., 140 (2000), 351398. 

3 
M. Anderson, Robust ergodic properties in partially hyperbolic dynamics, Trans. Amer. Math. Soc., 362 (2010), 18311867. 

4 
P. G. Barrientos, Y. Ki and A. Raibekas, Symbolic blenderhorseshoes and applications, Nonlinearity, 27 (2014), 28052839. 

5 
C. Bonatti and L. J. Díaz, Persistent nonhyperbolic transitive diffeomorphisms, Ann. of Math.(2), 143 (1996), 357396. 

6 
C. Bonatti and L. J. Díaz, Robust heterodimensional cycles and $C^1$generic dynamics, J. Inst. Math. Jussieu, 7 (2008), 469525. 

7 
C. Bonatti and L. J. Díaz, Abundance of $C^1$robust homoclinic tangencies, Trans. Amer. Math. Soc., 364 (2012), 51115148. 

8 
C. Bonatti, L. J. Díaz and R. Ures, Minimality of strong stable and unstable foliations for partially hyperbolic diffeomorphisms, J. Inst. Math. Jussieu, 1 (2002), 513541. 

9 
C. Bonatti, L. J. Díaz and M. Viana, Dynamics Beyond Uniform Hyperbolicity, Encyclopaedia Math. Sci., SpringerVerlag, 2005. 

10 
C. Bonatti and R. Potrie, Many intermingled basins in dimension 3, preprint, arXiv:1603.03803v1. 

11 
C. Bonatti and M. Viana, SRB measures for partially hyperbolic diffeomorphisms whose central direction is mostly contracting, Isreal J. of Math., 115 (2000), 157193. 

12 
R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math., 29 (1975), 181202. 

13 
K. Burns, F. R. Hertz, J. R. Hertz, A. Talitskaya and R. Ures, Density of accessibility for partially hyperbolic diffeomorphisms with onedimensional center, Discrete Contin. Dyn. Syst., 22 (2008), 7588. 

14 
D. Dolgopyat, M. Viana and J. Yang, Geometric and measuretheoretical structures of maps with mostly contracting center, Commun. Math. Phys., 341 (2016), 9911014. 

15 
S. Gan and Y. Shi, Topological mixing for Kan's map, In preparation. 

16 
M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathmatics, SpringerVerlag, Berlin, 1977. 

17 
A. J. Homburg and M. Nassiri, Robust minimality of iterated function systems with two generators, Ergod. Th. & Dynam. Sys., 34 (2014), 19141929. 

18 
J. E. Hutchinson, Fractals and selfsimilarity, Indiana Univ. Math. J., 30 (1981), 713747. 

19 
Y. S. Ilyashenko, V. A. Kleptsyn and P. Saltykov, Openness of the set of boundary preserving maps of an annulus with intermingled attracting basins, J. Fixed Point Theory Appl., 3 (2008), 449463. 

20 
I. Kan, Open sets of diffeomorphisms having two attractors, each with an everywhere dense basin, Bull. Amer. Math. Soc. (N.S.), 31 (1994), 6874. 

21 
V. A. Kleptsyn and P. S. Saltykov, On $C^2$stable effects of intermingled basins of attractors in classes of boundarypreserving maps, Trans. Moscow Math. Soc., (2011), 193217. 

22 
S. W. McDonald, C. Grebogi, E. Ott and J. A. Yorke, Fractal basin boundaries, Phys. D., 17 (1985), 125153. 

23 
M. Nassiri and E. Pujals, Robust transitivity in Hamiltonian dynamics, Ann. Sci. Éc. Norm. Supér., 45 (2012), 191239. 

24 
A. Okunev, Milnor attractors of skew products with the fiber a circle, J. Dyn. Control Syst., 23 (2017), 421433. 

25 
J. Palis, A global perspective for nonconservative dynamics, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 485507. 

26 
Y. Pesin and Y. Sinai, Gibbs measures for partially hyperbolic attractors, Ergod. Th. & Dynam. Sys., 2 (1982), 417438. 

27 
D. Ruelle, A measure associated with Axiom A attractors, Amer. J. Math., 98 (1976), 619654. 

28 
Ya. Sinai, Gibbs measures in ergodic theory, Russian Math. Surveys, 27 (1972), 2164. 

29 
R. Ures and C. H. Vasquez, On the robustness of intermingled basins, preprint, arXiv:1503.07155v2. 

30 
M. Viana and J. Yang, Physical measures and absolute continuity for onedimensional center direction, Ann. Inst. H. Poincaré Anal. Non Linéaire, 30 (2013), 845877. 

31 
J. Yang, Entropy along expanding foliations, preprint, arXiv:1601.05504v1. 

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