Anosov diffeomorphisms and expanding immersions. I

Jones, Lowell

doi:10.1090/S0002-9947-1985-0779055-7

Anosov diffeomorphisms and expanding immersions. I
HTML articles powered by AMS MathViewer

by Lowell Jones

Trans. Amer. Math. Soc. 289 (1985), 115-131

DOI: https://doi.org/10.1090/S0002-9947-1985-0779055-7

PDF | Request permission

Abstract:

The purpose of this paper is to develop a theory for representing Anosov diffeomorphisms by expanding immersions on compact branched manifolds. This theory was motivated by R. F. Williams’ study of expanding attractors [15,17].

References

D. V. Anosov, Geodesic flows on closed Riemannian manifolds of negative curvature, Trudy Mat. Inst. Steklov. 90 (1967), 209 (Russian). MR 0224110
Rufus Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin-New York, 1975. MR 0442989, DOI 10.1007/BFb0081279
F. T. Farrell and L. E. Jones, New attractors in hyperbolic dynamics, J. Differential Geometry 15 (1980), no. 1, 107–133 (1981). MR 602444, DOI 10.4310/jdg/1214435388
F. T. Farrell and L. E. Jones, Expanding immersions on branched manifolds, Amer. J. Math. 103 (1981), no. 1, 41–101. MR 601462, DOI 10.2307/2374189
John Franks, Anosov diffeomorphisms, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 61–93. MR 0271990
Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73. MR 623534, DOI 10.1007/BF02698687
John Guckenheimer, Endomorphisms of the Riemann sphere, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 95–123. MR 0274740
Lowell Jones, Locally strange hyperbolic sets, Trans. Amer. Math. Soc. 275 (1983), no. 1, 153–162. MR 678341, DOI 10.1090/S0002-9947-1983-0678341-7

Anosov diffeomorphism and expanding immersions

Clark Robinson and Robert Williams, Classification of expanding attractors: an example, Topology 15 (1976), no. 4, 321–323. MR 415682, DOI 10.1016/0040-9383(76)90024-0
Michael Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175–199. MR 240824, DOI 10.2307/2373276
Ja. G. Sinaĭ, Markov partitions and U-diffeomorphisms, Funkcional. Anal. i Priložen. 2 (1968), no. 1, 64–89 (Russian). MR 0233038
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
Dennis Sullivan and R. F. Williams, On the homology of attractors, Topology 15 (1976), no. 3, 259–262. MR 413185, DOI 10.1016/0040-9383(76)90041-0
R. F. Williams, One-dimensional non-wandering sets, Topology 6 (1967), 473–487. MR 217808, DOI 10.1016/0040-9383(67)90005-5

Classifications of

dimensional attractors

R. F. Williams, Expanding attractors, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 169–203. MR 348794, DOI 10.1007/BF02684369
John Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 32 (1958), 215–223. MR 95518, DOI 10.1007/BF02564579