Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Derivative formula of the potential function for generalized SRB measures of hyperbolic systems of codimension one
Pages: 967 - 983, Issue 3, March 2015

doi:10.3934/dcds.2015.35.967      Abstract        References        Full text (394.2K)           Related Articles

Miaohua Jiang - Department of Mathematics, Wake Forest University, Winston Salem, NC 27109, United States (email)

1 D. Anosov and Y. Sinai, Certain smooth ergodic systems, Russian Math. Surveys, 22 (1967), 107-172.       
2 L. Barreira, Thermodynamic Formalism and Applications to Dimension Theory, Progress in Mathematics, 294 Birkhäuser/Springer Basel AG, Basel, 2011.       
3 L. Barreira and Y. Pesin, Nonuniform Hyperbolicity, Encyclopedia of Mathematics and its Applications, 115 Cambridge University Press, Cambridge, 2007.       
4 V. Baladi and D. Smania, Linear response formula for piecewise expanding unimodal maps, Nonlinearity, 21 (2008), 677-711.       
5 V. Baladi and D. Smania, Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps, Ann. Sci. Éc. Norm. Supér. (4), 45 (2012), 861-926.       
6 D. Dolgopyat, On differentiability of SRB states for partially hyperbolic systems, Invent. Math., 155 (2004), 389-449.       
7 S. Gouëzel and C. Liverani, Banach spaces adapted to Anosov systems, Ergodic Theory Dynam. Systems, 26 (2006), 189-217.       
8 S. Gouëzel and C. Liverani, Compact locally maximal hyperbolic sets for smooth maps: Fine statistical properties, J. Differential Geom., 79 (2008), 433-477.       
9 M. Jiang, Differentiating potential functions of SRB measures on hyperbolic attractors, Ergodic Theory Dynam. Systems, 32 (2012), 1350-1369.       
10 M. Jiang and R. de la Llave, Smooth dependence of thermodynamic limits of SRB measures, Comm. Math. Physics, 211 (2000), 303-333.       
11 M. Jiang and R. de la Llave, Linear response function for coupled hyperbolic attractors, Comm. Math. Phys., 261 (2006), 379-404.       
12 A. Katok and B. Hasselblatt, Introduction to the Modern Theorey of Dynamical Systems, Cambridge University Press, Cambridge, 1995.       
13 R. Mañé, Erodic Theory and Differentiable Dynamics, Springer-Verlag, Berlin, 1987.       
14 A. A. Pinto and D. A. Rand, Smoothness of holonomies for codimension 1 hyperbolic dynamics, Bull. London Math. Soc., 34 (2002), 341-352.       
15 M. Pollicott and H. Weiss, The dimensions of some self-affine limit sets in the plane and hyperbolic sets, J. Statist. Phys., 77 (1994), 841-866.       
16 C. Pugh, M. Viana and A. Wilkinson, Absolute continuity of foliations, IMPA preprint, 2007, available at: http://w3.impa.br/~viana/out/pvw.pdf
17 D. Ruelle, Differentiation of SRB States, Commun. Math. Phys., 187 (1997), 227-241, Correction and complements, Comm. Math. Phys., 234 (2003), 185-190.       
18 D. Ruelle, Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics, J. Statist. Phys., 95 (1999), 393-468.       
19 D. Ruelle, Thermodynamic Formalism, The mathematical structures of equilibrium statistical mechanics. Second edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2004.       
20 Y. G. Sinai, Topics in Ergodic Theory, Princeton Mathematical Series, 44 Princeton University Press, Princeton, N.J., 1994.       
21 J. Schmeling, Hölder continuity of the holonomy maps for hyperbolic basic sets. II, Math. Nachr., 170 (1994), 211-225.       

Go to top