Citation: |
[1] |
S. K. Aranson, G. R. Belitsky and E. V. Zhuzhoma, Introduction to the Qualitative Theory of Dynamical Systems on Surfaces, American Mathematical Society, Providence, RI, 1996. |
[2] |
M. Baake and J. A. G. Roberts, Reversing symmetry group of $ Gl(2,\mathbbZ)$ and $ PGl(2,\mathbbZ)$ matrices with connections to cat maps and trace maps, J. Phys. A, 30 (1997), 1549-1573.doi: 10.1088/0305-4470/30/5/020. |
[3] |
L. Barreira and Y. Pesin, Nonuniform Hyperbolicity, Mathematics and its Applications, Cambridge University Press, Cambridge, 2007.doi: 10.1017/CBO9781107326026. |
[4] |
L. Barreira, Y. Pesin and J. Schmeling, Dimension and product structure of hyperbolic measures, Ann. of Math. (2), 149 (1999), 755-783.doi: 10.2307/121072. |
[5] |
A. W. Brown, Rigidity Properties of Measures on the Torus, Ph.D thesis, Tufts University, 2011. |
[6] |
M. Einsiedler and E. Lindenstrauss, Rigidity properties of $\mathbbZ^d$-actions on tori and solenoids, Electron. Res. Announc. Amer. Math. Soc., 9 (2003), 99-110.doi: 10.1090/S1079-6762-03-00117-3. |
[7] |
J. Franks, Anosov diffeomorphisms, in Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, 61-93. |
[8] |
B. Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergodic Theory Dynam. Systems, 14 (1994), 645-666.doi: 10.1017/S0143385700008105. |
[9] |
H. Hu, Some ergodic properties of commuting diffeomorphisms, Ergodic Theory Dynam. Systems, 13 (1993), 73-100.doi: 10.1017/S0143385700007215. |
[10] |
B. Kalinin and A. Katok, Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori, J. Mod. Dyn., 1 (2007), 123-146. |
[11] |
B. Kalinin, A. Katok and F. Rodriguez Hertz, Nonuniform measure rigidity, Ann. of Math. (2), 174 (2011), 361-400.doi: 10.4007/annals.2011.174.1.10. |
[12] |
A. Katok and R. J. Spatzier, Invariant measures for higher-rank hyperbolic abelian actions, Ergodic Theory Dynam. Systems, 16 (1996), 751-778.doi: 10.1017/S0143385700009081. |
[13] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995.doi: 10.1017/CBO9780511809187. |
[14] |
F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms. II. Relations between entropy, exponents and dimension, Ann. of Math. (2), 122 (1985), 540-574.doi: 10.2307/1971329. |
[15] |
R. Mañé, Ergodic Theory and Differentiable Dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Springer-Verlag, Berlin, 1987.doi: 10.1007/978-3-642-70335-5. |
[16] |
A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math., 96 (1974), 422-429.doi: 10.2307/2373551. |
[17] |
S. E. Newhouse, On codimension one Anosov diffeomorphisms, Amer. J. Math., 92 (1970), 761-770.doi: 10.2307/2373372. |
[18] |
V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč., 19 (1968), 179-210. |
[19] |
J. C. Oxtoby and S. M. Ulam, Measure-preserving homeomorphisms and metrical transitivity, Annals of Mathematics. Second Series, 42 (1941), 874-920.doi: 10.2307/1968772. |
[20] |
J. Palis, C. Pugh and R. C. Robinson, Nondifferentiability of invariant foliations, in Dynamical Systems-Warwick 1974, Springer, (1975), 234-240. |
[21] |
C. Pugh, M. Shub and A. Wilkinson, Hölder foliations, Duke Math. J., 86 (1997), 517-546.doi: 10.1215/S0012-7094-97-08616-6. |
[22] |
V. A. Rohlin, On the fundamental ideas of measure theory, Amer. Math. Soc. Translation, 1952 (1952), 55 pp. |
[23] |
D. J. Rudolph, $\times 2$ and $\times 3$ invariant measures and entropy, Ergodic Theory Dynam. Systems, 10 (1990), 395-406.doi: 10.1017/S0143385700005629. |