- (with L. Barreira) Lectures on Lyapunov Exponents and Smooth Ergodic Theory, in the book: "Smooth Ergodic Theory and Its Applications", AMS, Proceedings of Symposia in Pure Mathematics (2001) 3--90.
- Dynamical Systems With Generalized Hyperbolic Attractors: Hyperbolic, Ergodic and Topological Properties, Ergod. Theory and Dyn. Syst., 12:1 (1992) 123-152.
- (with M. Brin) On Morse-Smale Endomorphisms (pdf), Amer. Math. Soc. Transl., 171:2 (1996) 35-43.
- (with R. de la Llave and M. Jiang) On the Integrability of Intermediate Foliations for Anosov Diffeomorphisms, Ergod. Theory and Dyn. Syst., 15:2 (1995) 317-331.
- (with D. Dolgopyat and H. Hu) An Example of a Smooth Hyperbolic Measure with Countably Many Ergodic Components (pdf), Appendix to "Lectures on Lyapunov Exponents and Smooth Ergodic Theory" (pdf) in the book: "Smooth Ergodic Theory and Its Applications", Proceedings of Symposia in Pure Mathematics (2001) 95--106.
- (with D. Dolgopyat and K. Burns) Partial Hyperbolicity, Lyapunov Exponents and Stable Ergodicity ( pdf), J. Stat. Phys., 108, no. 5-6 (2002) 927--942.
- (with D. Dolgopyat , K. Burns and M. Pollicott ) Stable Ergodicity For Partially Hyperbolic Attractors With Negative Central Exponents
(pdf), Journal of Modern Dynamics, v. 2, no.1 (2008) 1--19.
- (with M. Hirayama) Non-absolutely Continuous Foliations (pdf), Israel Journal of Math., 160 (2007) 173--187.
- On the Work of Dolgopyat on Partial and Nonuniform Hyperbolicity (pdf), Journal of Modern Dynamics v. 4, N2 (2010) 227-241.
- (with V. Climenhaga ), Hadamard--Perron Theorems and Effective Hyperbolicity (pdf)
Preprint, PSU 2013.
- (with V. Climenhaga , D. Dolgopyat ), Non-stationary Non-uniform Hyperbolicity: SRB Measures For Dissipative Maps (pdf) Preprint, PSU 2013.
# 2. Genericity and Coexistence

- (with D. Dolgopyat ) Every Compact Manifold Carries a Completely Hyperbolic Diffeomorphism (pdf), Ergod. Th. and Dyn. Syst., 22 (2002) 1--27.
- (with H. Hu and A. Talitskaya) Every Compact Manifold Carries a Hyperbolic Bernoulli Flow (pdf), in the book: "Modern Dynamical Systems and Applications", Cambridge Univ. Press, 2004, pp. 347--358.
- Existence and Genericity Problems for Dynamical Systems with Nonzero Lyapunov Exponents (pdf), Regular and Chaotic Dynamics, 12, no. 5 (2007) 476--489.
- (with H. Hu and A. Talitskaya), A Volume Preserving Diffeomorphism With Essential Coexistence of Zero and Nonzero Lyapunov Exponents (pdf), CMP, v. 319, N2 (2013) 331-378.
- (with J. Chen and H. Hu ), A Volume Preserving Flow With Essential Coexistence of Zero and Nonzero Lyapunov Exponents (pdf), ETDS 2013 (to appear).
# 3. Mathematical Physics. Coupled Map Lattices

- (with Ya. Sinai) Space-time Chaos In Chains Of Weakly Interacting Hyperbolic Mappings, Advances in Soviet Math., 3 (1991) 165-198.
- (with M. Jiang) Equilibrium Measures for Coupled Map Lattices: Existence, Uniqueness, and Finite-Dimensional Approximations (pdf), Comm. Math. Phys., 193:3 (1998) 675-711.
- (with V. Afraimovich) Traveling Waves in Lattice Models of Multi-Dimensional and Multi-Component Media: Part I. General Hyperbolic Properties, Nonlinearity, 6 (1993) 429-455.
- (with V. Afraimovich and
A. Tempelman) Traveling Waves in Lattice Models of Multi-Dimensional and Multi-Component Media: Part II. Ergodic Properties and Dimension, Chaos 3 (1993) 233-2412.
- (with D. R. Orendovici) Chaos in Traveling Waves of Lattice Systems of Unbounded Media (pdf), Proceedings of the IMA Volumes in Mathematics and its Applications, v. 119, "Numerical Methods for Bifurcation Problems and Large-scale Dynamical Systems", Springer-Verlag (1999) 327-359.
- (with A. Yurchenko) Some Physical Models of The Reaction-Diffusion Equation and Coupled Map Lattices (pdf), Russian Math. Surveys, 59, n.3, 2004.
- (with H. Kang) Dynamics of a Discrete Brusselator Model:
Escape to infinity and Julia set (pdf), Milan Journal of Mathematics, 73 (2004), 1--15.
# 4. Thermodynamic Formalism

- (with Ke Zhang) Phase Transitions For Uniformly Expanding Maps (pdf), J. Stat. Phys., 122:6 (2006), 1095--1110.
- (with Ke Zhang) Thermodynamics Associated With Inducing Schemes and Liftability of Measures (pdf), Proc. Fields Inst., 51 (2007) 289--305.
- (with S. Senti)
Equilibrium Measures for Maps with Inducing Schemes (pdf), Journal of Modern Dynamics v. 2, no. 3 (2008) 1--31.
- (with S. Senti and Ke Zhang) Lifting Measures to Inducing Schemes (pdf), Ergod. Th. and Dyn. Syst.,v. 28:2 (2008) 553--574.
- (with S. Senti and Ke Zhang) Thermodynamics of Towers of Hyperbolic Type (pdf), Preprint, PSU, 2010.
# 5. Dimension Theory. Multifractal Formalism

- On Rigorous Mathematical Definition of Correlation Dimension and Generalized Spectrum For Dimensions, J. Stat. Phys., 71:3-4 (1993) 529-547.
- (with A. Tempelman) Correlation Dimension of Measures Invariant Under Group Actions (pdf), Random and Computational Dynamics,
3:3 (1995) 137-156.
- (with L. Barreira and J. Schmeling) On a General Concept of Multifractality: Multifractal Spectra for Dimensions, Entropies, and Lyapunov Exponents. Multifractal Rigidity (pdf), Chaos, 7:1 (1997) 27-3.
- (with L. Barreira and J. Schmeling) Multifractal Spectra and Multifractal Rigidity for Horseshoes (pdf), Journal of Dynamical and Control Systems, 3:1 (1997) 33-49.
- (with H. Weiss) On the Dimension of Deterministic and Random Cantor-like Sets, Symbolic Dynamics, and the Eckmann-Ruelle Conjecture, Comm. Math. Phys., 182:1 (1996) 105-153.
- (with H. Weiss)
A Multifractal Analysis of Equilibrium Measures For Conformal Expanding Maps and Markov Moran Geometric Constructions (pdf), J. Stat. Phys., 86:1-2 (1997) 233-275.
- (with H. Weiss)
The Multifractal Analysis of Gibbs Measures: Motivation, Mathematical Foundation, and Examples (pdf), Chaos, 7:1 (1997) 89-106.
- (with L. Barreira and J. Schmeling) Dimension and Product Structure of Hyperbolic Measures (pdf), Annals of Math., 149:3 (1999) 755-783.
- Entropy and Dimension Families Associated with Equilibrium Measures for Hyperbolic Dynamical Systems (pdf), Progress in Probability, Birhauser, 46 (2000) 209-223.
- (with V. Sadovskaya) Multifractal Analysis of Conformal
Axion A Flows (pdf), Comm. Math. Phys., 216:2 (2001) 277-312.
- (with H. Weiss ) The Multifractal Analysis of Birkhoff Averages and Large Deviations
(pdf), in the book "Global Analysis of Dynamical Systems", Editors: H. Broer, B. Krauskopf, G. Vegter. IoP Publishing, Bristol, UK, 2001.
- (with J. Chen)
Dimension of Non-conformal Repellers: a Survey
(pdf), Nonlinearity, v. 23, N4 (2010).
- (with Y. Zhao) Scaled Entropy for Dynamical Systems (pdf), Preprint, 2014.