 Entropy of continuous flows on compact 2manifolds,
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 On the prevalence of horseshoes, Trans. AMS, 263, 1981, 7588.
 A closing lemma on the interval, Invent. Math., 54, 1979, 179187.
 (with L. Block, J. Guckenheimer and M. Misiurewicz) Periodic points
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 (with C. Robinson) Nonabsolutely continuous foliations for an Anosov diffeomorphism, Invent. Math., 61, 1980, 159176.
 (with J. Franks) A $C^2$ KupkaSmale diffeomorphism of the disk
with no sources or sinks, Proc. Warwick Symp, Springer Lecture Notes in Math., 898, 1981, 9098.
 (with S. Newhouse) Dynamics of certain skew products,
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 (with D. Rand) Dynamical Systems and Turbulence, Warwick 1980,
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 Capacity of attractors, Ergod. Thy & Dynam. Sys., 1, 1981,
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{\bf 30}, 1983, 599606.
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 Dimension, entropy and Lyapunov exponents in differentiable dynamical systems, Physica A, 124, 1984, 639646. (text of lecture at International
Congress of Math Phys., Boulder 1983)
 (with F. Ledrappier) The metric entropy of diffeomorphisms, Part I: Characterization of measures satisfying Pesin's entropy formula, Annals Math., 122, (1985), 509539.
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 (with F. Ledrappier) The metric entropy of diffeomorphisms, Part II: Relations between entropy, exponents and dimension, Annals Math., 122, (1985), 540574.
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 Stochastic stability of hyperbolic attractors, Ergod. Th. & Dynam. Sys., 6, (1986), 311319.
 Random perturbations of matrix cocycles, Ergod. Th. & Dynam. Sys.,
6, (1986), 627637.
 (with F. Ledrappier) Entropy formula for random transformations, Prob. Th. Rel. Fields, 80, (1988), 217240.
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 Some large deviation results for dynamical systems, Trans. AMS,
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 (with F. Ledrappier) Stability of Lyapunov exponents, Ergod. Th. & Dynam. Sys., 11, (1991), 469484.
 (with P. Thieullen and C. Tresser) Exposant de Lyapunov positif dans
des familles a un parametre d'applications unimodales, C.R. Acad. Sci.
Paris, 315.I, (1992), 6972; J d'Analyse, 64, (1994), 121172.
 (with M. Benedicks) Absolutely continuous invariant measures and random perturbations of certain onedimensional maps, Ergod. Th. & Dynam. Sys,
12, (1992), 1337.
 Decay of correlations for certain quadratic maps, Commun. Math. Phys, 146, (1992), 123138.
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 (with M. Benedicks) SinaiBowenRuelle measures for certain Henon maps, Invent. Math, 112, (1993), 541576.
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 Ergodic theory of chaotic dynamical systems, Proc. of SMALEFEST, SpringerVerlag, (1993), 201226.
 Some open sets of nonuniformly hyperbolic cocycles, Ergod. Th. & Dynam.
Sys., 13, (1993), 409415.
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 (with V. Baladi) On the spectra of randomly perturbed expanding maps, Commun. Math. Phys., 156, (1993), 355385.
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 (with H. Hu) Nonexistence of SBR measures for some diffeomorphisms that are ``almost Anosov", Ergod. Th. & Dynam. Syst., 15, (1995), 6776.
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 Ergodic theory of differentiable dynamical systems, "Real and Complex Dynamics", Ed. Branner and Hjorth, NATO ASI series, Kluwer Academic Publishers, (1995), 293336.
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 (with I. Klapper) Rigorous bounds on the fast dynamo growth rate involving topological entropy, Commun. Math Phys., 173, (1995), 623646.
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 Ergodic theory of attractors, Proceedings of the International
Congress of Mathematicians, Z\"urich, Switzerland 1994, Birkh\"auser Verlag, 1995, 12301237. (text of lecture)
 Developments in chaotic dynamics, AMS Notices, Nov. 1998.
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 Lyapunov exponents for some quasiperiodic cocycles, Ergod. Th. & Dynam. Syst., 17, (1997), 483504
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 Statistical properties of dynamical systems with some hyperbolicity, Annals of Math., (1998), 585650
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 (with R. Murray and M. Keane) Computing invariant measures for
expanding circle maps, Nonlinearity 1998.
 Ergodic theory of chaotic dynamical systems, Proc.
International Congress of Math. Phys., Brisbane 1997,
International Press (1999), 132143.
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 Developments in chaotic dynamics, AMS Notices, Nov. 1998.
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 (with M. Benedicks) Markov extensions and decay of correlations for certain Henon maps, Asterisque 261, (2000), 1356.
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 Recurrence times and rates of mixing, Israel J Math.
110, (1999), 153188
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 Geometric and ergodic theory of hyperbolic dynamical systems,
Lecture series in Current Developments in Mathematics 1998, HarvardMIT,
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 (with Q.D. Wang) Strange attractors with one direction of instability,
Commun. Math. Phys. 218, (2001), 197.
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 (with N. Chernov) Decay of correlations for Lorentz gases and
hard balls, Encycl. of Math. Sc., Math. Phys. II, Vol. 101, Ed. Szasz,
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 (with Q.D. Wang) From invariant curves to strange attractors,
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 (with N. Masmoudi) Ergodic theory of infinite dimensional systems
with applications to dissipative parabolic PDEs, Commun.
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 Entropy in dynamical systems, in Entropy, Ed. Greven Keller and Warnecke, Princeton Univ. Press, (2003), 313328.
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 What are SRB measures, and which dynamical systems
have them?, J. Stat. Phys., vol. 108, Issue 5, (2002), 733754.
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 (with Q.D. Wang) Strange attractors in periodicallykicked limit
cycles and Hopf bifurcations, Commun. Math. Phys. 240, (2003),
509529.
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 Board of Advisors and contributor to Encyclopedia of Nonlinear Science,
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(with W. Cowieson) SRB measures as zeronoise limits, Ergod. Th. & Dynam. Sys.,
Vol. 25, 4, (2005) 10911113.
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 (with J.P. Eckmann) Temperature profiles in Hamiltonian heat conduction,
Europhysics Letters, Volume 68, Issue 6, December 2004, 790796.
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(with J.P. Eckmann) Nonequilibrium energy profiles for a class of 1D models,
Commun. Math. Phys. Vol. 262, No. 1 (2006) 237267.
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(with Q.D. Wang) Nonuniformly expanding 1D maps, Commun. Math. Phys. Vol. 264,
No.1 (2006) 255282.
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(with M. Demers) Escape rates and conditionally invariant measures, Nonlinearity 19 (2006) 377397.
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(with J. Guckenheimer and M. Weschelberger) Chaotic attractors of relaxation
oscillators, Nonlinearity 19, No. 3 (2006) 701720.
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(with K. Lin) Correlations in Nonequilibrium Steady States
of Random Halves Models, J. Stat. Phys., Vol. 128, No. 3, (2007), 607639.

(with K. Ravishankar) Local Thermodynamic Equilibrium for
some Stochastic Models of Hamiltonian Origin, J Stat. Phys., Vol. 128, No. 3, (2007), 641665.

(with E. Kobre) Extended Systems with Deterministic Local Dynamics
and Random Jumps, Commun. Math. Phys., Vol, 275, No.3, (2007), 709720

(with Q.D. Wang) Toward a theory of rank one attractors,
Annals of Math, Vol 167. No.2 (2008) 349480.
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(with L. ReyBellet) Large Deviations in nonuniformly hyperbolic dynamical
systems, Ergod Th & Dynam Sys, Vol. 28, Issue 02, (2008), 587612.

(with K. Lin) Shearinduced chaos, Nonlinearity 21 (2008) 899922.
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Chaotic phenomena in three settings: large, noisy, and out of equilibrium,
Nonlinearity 21 (2008) T245T252 (invited article "Open Problems").
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(with W. Ott and M. Stenlund) Memory loss for timedependent
dynamical systems, Math. Res. Lett. 16 (2009), no. 3, 463475.
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Postscript ]

(with K. Lin and E. SheaBrown) Reliability of coupled oscillators,
J. Nonlin. Sci., 19, 2009, 497545.
[ PDF published version ]

(with K. Lin and E. SheaBrown) SpikeTime Reliability of
Layered Neural Oscillator Networks, J. Comp. Neurosci., 27, 2009, 135160.
[ PDF preprint version ]

(with K. Lin and E. SheaBrown) Reliability of layered neural oscillator
networks, Comm. Math. Sci., 7, 2009, 239247 (rapid communication).

(with S. Mintchev) Selforganization in predominantly feedforward
oscillator chains, Chaos, 2009, no. 4, 043131, 10pp.

(with P. Balint and K. Lin) Ergodicity and energy distributions for
some boundary driven integrable Hamiltonian chains, Commun. Math. Phys., Vol 294, 1, 2010, 199228.
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(with M. Demers and P. Wright) Escape rates and physically relevant measures for
billiards with small holes, Commun. Math. Phys., Vol 294, 2, 2010, 353338.

(with J. Koiller) Coupled map networks, Nonlinearity, 23, 5, 2010, 11211141.
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(with K. Lin) Nonequilibrium steady states for certain Hamiltonian models, J. Stat. Phys. 139 no. 4, 2010, 630657.

(with K. Lin) Dynamics of periodicallykicked oscillators, J. Fixed Point Theory Appl., 7 no. 2, 2010, 291312.

(with J.P. Eckmann) Rattling and freezing in a 1D transport model, Nonlinearity 24 (2011) 207226.

(with K. Lu and Q.D. Wang) Strange attractors for periodically forced parabolic equations, AMS Memoirs (2013).

(with Z. Lian) Lyapunov exponents, periodic orbits and horseshoes for mappings of Hilbert spaces, Ann. Henri Poincaré 12, 2011, 10811108.

(with M. Demers and P. Wright) Entropy, Lyapunov exponents and escape rates
in open systems, Ergod Th & Dynam Sys, 32:4 (2012), 12701301.

(with Q.D. Wang) Dynamical profile of a class of rankone attractors,
Ergod. Th. & Dynam. Sys, Ergod. Th. & Dynam. Sys, Vol 33, Issue 04, (2013) p.12211264.

(with Z. Lian) Lyapunov exponents, periodic orbits and horseshoes for
semiflows of Hilbert spaces, J. Amer. Math. Soc. 25 (2012), 637665.

(with B. Ryals) Horseshoes of periodicallykicked van der Pol oscillators, Chaos 22, (2012) 043140.
(with K. Lin, K.C.A. Wedgewood and S. Coombes) Limitations of
perturbative techniques in the analysis of rhythms and oscillations, J. Math. Biol. 66 (2013) 139161.

(with B. Ryals) Nonequilibrium steady states of some simple 1D
mechanical chains, J. Stat. Phys. Vol. 146, No. 5, 2012, 10891103
(with Z. Lian and C. Zeng) Absolute continuity of stable foliations for
systems on Banach spaces, J Diff. Equations, Vol. 254, 1, (2013) 283308.
(with A. Rangan) Emergent dynamics in a model of visual cortex, J Comp. Neurosci., Vol 35, Issue 2, 155167 (2013).
(with A. Rangan) Dynamics of spiking neurons: between homogeneity and
synchrony, J Comp. Neurosci., Volume 34, Issue 3 (2013), Page 433460.
Understanding chaotic dynamical systems, (invited article), Commun. Pure & Appl. Math. Vol 66, Issue 9 (2013), 14391462.
(with M. Stenlund and H. Zhang) Dispersing billiards with moving scatterers, Commun. Math. Phys. Vol. 322, Issue 3 (2013), 909955.
Mathematical theory of Lyapunov exponents, (invited review article), J. Phys. A: Math Theor. 46 (2013) 254001.
(with A. Barrat, B. Fernandez and K. Lin) Modeling temporal networks using random itineraries, Phys. Rev. Lett. 110 (2013), article no 158702.
(with Y. Li) Existence of nonequilibrium steady state for a simple model
of heat conduction, J Stat Phys., 152 (2013) 117093.
(with Y. Li) Nonequilibrium steady states for a class of particle systems,
Nonlinearity 27 (2014) 607636.
(with L. Chariker) Emergent spike patterns in neuronal populations, J Comp. Neur
osci. (2015) 38:203220.
(with T. Pereira) Control of epidemics on complex networks: effectiveness
of delayed isolation, Phys. Rev. E, 92, 022822 (2015).
(with Y. Li and P. Nandori) Local thermal equilibrium for certain stochastic mod
els of heat transport, J Stat Phys. 163 (2016) 1: 6191.

(with Y. Li) Polynomial convergence to equilibrium for a system of interacting
particles, Annals of Applied Prob. 27(1), (2017) 6590

(with A. Blumenthal) Entropy, volume growth and SRB measures for Banach space
mappings, Invent. Math. 207 No.2 (2017) 833893
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(with G. Lajoie) Dynamic signal tracking in a simple V1 spiking model, Neural Comp. 28 (2016) 19852010.

(with A. Blumenthal and J. Xue) Lyapunov exponents for random perturbations of some areapreserving maps including the standard map, Annals of Math, 185 (2017) 126
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(with A. Blumenthal) Absolute continuity of stable foliations for mappings of Banach spaces, Commun. Math. Phys. (2017) 354:591619

(with L. Chariker and R. Shapley) Orientation selectivity from very sparse LGN inputs in a comprehensive model of macaque V1 cortex, J Neurosci (2016) 36(49):1236812384

Generalizations of SRB measures to nonautonomous, random, and infinite dimensional systems, J. Stat. Phys. (2017) 166:494515

Unraveling the dynamics of the Brain through modeling and analysis, Patterns of Dynamics, Springer Proc. Math. & Stat., Ed Gurevich et al (2017) p.393

(with A. Blumenthal and J. Xue) Lyapunov exponents and correlation decay for random perturbations of some prototypical 2D maps, Commun. Math. Phys. (2018) 359:347373

(with Y. Li and L. Chariker) How well do reduced models capture the dynamics in models of interacting neurons? J. Math. Biol. published online (2018)

(with A. Blumenthal) Equivalence of physical and SRB measures in random dynamical systems, 2018 preprint

(with L. Chariker and R. Shapley) Rhythm and synchrony in a cortical network model, to appear in J. Neurosci. (2018)

(with S. Ruschel, T. Pereira and S. Yanchuk) SIQ: A delay differential equations model for disease control via isolation, 2018 preprint

(with S. Ruschel, T. Pereira and S. Yanchuk) Isolation as a means of epidemcis control: consequences of delays and imperfect implementation, 2018 preprint

Comparing chaotic and random dynamical systems, to appear in Proc. ICMP 2018 Montreal, 2018 preprint

Dynamical systems evolving, Proc. ICM 2018 Rio de Janeiro, World Scientific (2018)
