Journal of Modern Dynamics (JMD)

Nonexpanding attractors: Conjugacy to algebraic models and classification in 3-manifolds
Pages: 517 - 548, Issue 3, July 2010

doi:10.3934/jmd.2010.4.517      Abstract        References        Full text (357.1K)           Related Articles

Aaron W. Brown - Department of Mathematics, Tufts University, Medford, MA 02155, United States (email)

1 C. Bonatti, Problem in dynamical systems, http://www.math.sunysb.edu/dynamics/bonatti_prob.txt, November 1999.
2 H. G. Bothe, Expanding attractors with stable foliations of class $C^0$, in "Ergodic theory and related topics, III," Lecture Notes in Math., 1514, Springer, Berlin, (1992), 36-61.       
3 B. Brenken, The local product structure of expansive automorphisms of solenoids and their associated $C^$*-algebras, Canad. J. Math., 48 (1996), 692-709.       
4 A. Brown, Constraints on dynamics preserving certain hyperbolic sets, Ergodic Theory Dynam. Systems, to appear.
5 T. Fisher, Hyperbolic sets with nonempty interior, Discrete Contin. Dyn. Syst., 15 (2006), 433-446.       
6 J. Franks, Anosov diffeomorphisms, in "Global Analysis," Amer. Math. Soc., Providence, R.I., 1970, 61-93.       
7 V. Z. Grines, V. S. Medvedev, and E. V. Zhuzhoma, On surface attractors and repellers in 3-manifolds, Mat. Zametki, 78 (2005), 813-826.       
8 B. G√ľnther, Attractors which are homeomorphic to compact abelian groups, Manuscripta Math., 82 (1994), 31-40.       
9 K. Hiraide, A simple proof of the Franks-Newhouse theorem on codimension-one Anosov diffeomorphisms, Ergodic Theory Dynam. Systems, 21 (2001), 801-806.       
10 W. Hurewicz and H. Wallman, "Dimension Theory," Princeton University Press, Princeton, N. J., 1941.       
11 B. Jiang, S. Wang, and H. Zheng, No embeddings of solenoids into surfaces, Proc. Amer. Math. Soc., 136 (2008), 3697-3700.       
12 J. L. Kaplan, J. Mallet-Paret, and J. A. Yorke, The Lyapunov dimension of a nowhere differentiable attracting torus, Ergodic Theory Dynam. Systems, 4 (1984), 261-281.       
13 A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems," Cambridge University Press, Cambridge, 1995.       
14 A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429.       
15 S. E. Newhouse, On codimension one Anosov diffeomorphisms, Amer. J. Math., 92 (1970), 761-770.       
16 R. V. Plykin, The topology of basic sets of Smale diffeomorphisms, Math. USSR-Sb., 13 (1971), 297-307.       
17 R. V. Plykin, Hyperbolic attractors of diffeomorphisms, Russian Math. Surveys, 35 (1980), 109-121.       
18 R. V. Plykin, Hyperbolic attractors of diffeomorphisms (the nonorientable case), Russian Math. Surveys, 35 (1980), 186-187.       
19 D. Ruelle and D. Sullivan, Currents, flows and diffeomorphisms, Topology, 14 (1975), 319-327.       
20 S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.       
21 R. F. Williams, One-dimensional non-wandering sets, Topology, 6 (1967), 473-487.       
22 R. F. Williams, Classification of one dimensional attractors, in "Global Analysis," Amer. Math. Soc., Providence, R.I., 1970, 341-361.       
23 R. F. Williams, Expanding attractors, Inst. Hautes √Čtudes Sci. Publ. Math., (1974), 169-203.       

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