My research interests are in dynamical systems
and ergodic theory, particularly nonuniform
hyperbolicity, thermodynamic formalism, dimension
theory, and multifractal analysis. Here you
can find my papers and preprints, information on
books I've written, and slides for talks I've
given.
I also maintain a research
blog, where I occasionally post about things
that I find interesting but that for one reason or
another don't fit (yet) into anything else I might
write. PDFs of some posts are linked to at
right.
List of publications
also available via MathSciNet
or BibServer
(not updated as frequently).
My research is
supported by the following grants:
 20162021: NSF
DMS1554794, "CAREER: Unifying approaches
to nonuniform hyperbolicity"
 20142017: NSF
DMS1362838, "Thermodynamics and
statistics of nonuniformly hyperbolic dynamical
systems"
See here for a
list of known corrections to the material below.
Papers. Survey/expository
papers are marked; all others are research papers.
 SRB
and equilibrium measures via dimension theory
Preprint, submitted.
 Beyond
Bowen's specification property
(Survey)  with Daniel J. Thompson.
Preprint, submitted.
 Closed
geodesics on surfaces without conjugate points
 with Gerhard Knieper and Khadim War.
Preprint, submitted.
 SRB measures and
Young towers for surface diffeomorphisms
 with Stefano Luzzatto and Yakov Pesin.
Preprint, submitted.
 Uniqueness
of the measure of maximal entropy for geodesic
flows on certain manifolds without conjugate
points
 with Gerhard Knieper and Khadim War.
Advances in Mathematics, to
appear.
 Equilibrium
measures for some partially hyperbolic systems
 with Yakov Pesin and Agnieszka
Zelerowicz.
Journal of Modern Dynamics, 16
(2020), 155205.
 Positive
entropy equilibrium states.
 with Van Cyr.
Israel Journal of Mathematics, 232
(2019), no. 2, 899920.
 Onesided almost
specification and intrinsic ergodicity.
 with Ronnie Pavlov.
Ergodic Theory and Dynamical Systems, 39
(2019), 24562480.
 Equilibrium states
for Mañé diffeomorphisms.
 with Todd Fisher and Daniel J. Thompson.
Ergodic Theory and Dynamical Systems, 39
(2019), 24332455.
 Equilibrium
states in dynamical systems via geometric
measure theory
(Survey)  with Yakov Pesin and Agnieszka
Zelerowicz.
Bulletin of the American Mathematical Society,
56
(2019), no. 4, 569610.
 Specification
and towers in shift spaces.
Communications in Mathematical Physics, 364,
issue 2 (2018), 441504.
 Unique equilibrium
states for geodesic flows in nonpositive
curvature.
 with Keith Burns, Todd Fisher, and
Daniel J. Thompson.
Geometric and Functional Analysis, 28
(2018), no. 5, 12091259.
 Unique equilibrium
states for BonattiViana diffeomorphisms.
 with Todd Fisher and Daniel J. Thompson.
Nonlinearity, 31
(2018), no. 6, 25322570.
 An earlier
version also studied the Mañé
examples; these were removed from the
final version and now appear in their own
paper
 Large deviations for
systems with nonuniform structure.
 with Daniel J. Thompson and Kenichiro
Yamamoto.
Transactions of the American Mathematical
Society, 369
(2017), no. 6, 41674192.
 The
geometric approach for constructing
SinaiRuelleBowen measures
(Survey)  with Stefano Luzzatto and Yakov
Pesin.
Journal of Statistical Physics, 166
(2017), 467493.
 Building
thermodynamics for nonuniformly hyperbolic
maps
(Survey)  with Yakov Pesin.
Arnold Mathematical Journal, 3
(2017), 3782.
 Unique equilibrium
states for flows and homeomorphisms with
nonuniform structure.
 with Daniel J. Thompson.
Advances in Mathematics, 303
(2016), 745799.
 Nonstationary
nonuniform hyperbolicity: SRB measures for
nonuniformly hyperbolic attractors.
 with Dmitry Dolgopyat and Yakov
Pesin.
Communications in Mathematical Physics, 346,
issue 2 (2016), 553602.
 HadamardPerron
theorems and effective hyperbolicity.
 with Yakov Pesin.
Ergodic Theory and Dynamical Systems, 36
(2016), 2363.
 Intrinsic
ergodicity via obstruction entropies.
 with Daniel J. Thompson.
Ergodic Theory and Dynamical Systems, 34
(2014), 18161831.
 The
thermodynamic approach to multifractal
analysis.
Ergodic Theory and Dynamical Systems, 34
(2014), 14091450.
 Topological
pressure
of simultaneous level sets.
Nonlinearity
26 (2013),
241268.
 Equilibrium
states beyond specification and the Bowen
property.
 with Daniel J. Thompson.
Journal of the
London Mathematical Society 87
(2013), 401427.
 Intrinsic
ergodicity beyond specification: βshifts,
Sgap shifts, and their factors.
 with Daniel J. Thompson.
Israel Journal
of Mathematics, 192
(2012), 785817.
 Bowen's
equation in the nonuniform setting.
Ergodic Theory
and Dynamical Systems 31 (2011),
11631182.
 Multifractal
formalism
derived
from thermodynamics for general dynamical
systems.
Electronic Research Announcements in
Mathematical Sciences 17 (2010),
111.
 A note on two
approaches to the thermodynamic formalism.
Discrete and
Continuous Dynamical Systems 27 (2010),
9951005.
 Open problems
in the theory of nonuniform hyperbolicity
(Survey)  with Yakov Pesin.
Discrete and
Continuous Dynamical Systems, 27 (2010),
589607.
 Measure theory
through dynamical eyes
(Expository)  with Anatole Katok.
Permanent preprint.
Books.
Talks. (Past and upcoming)
 June 23, 2020, University of Utah online
working seminar in ergodic theory
"Specification and the measure of
maximal entropy"
(Board
notes) (Notes on my
blog, or in pdf)
 March 9, 2020, Ohio State
"Nonadapted measures for billiards and other
systems with singularities"
 December 10, 2019, CIRM, Marseille (Thermodynamic
Formalism: Dynamical Systems, Statistical
Properties and their Applications)
"Closed geodesics and the measure of maximal
entropy on surfaces without conjugate points"
 September 29, 2019, Penn State (Workshop
in Dynamical Systems and Related Topics)
"Counting closed geodesics on surfaces
without conjugate points"
 July 26, 2019, University of Warwick (Thermodynamic
Formalism: Ergodic Theory and Geometry)
"BowenMargulis measure for geodesic flows"
(Slides)
 July 15, 2019, AIM, San Jose (Equilibrium
states for dynamical systems arising from
geometry)
"Equilibrium states and nonuniform
specification" (Video)
 May 1317, 2019, CIRM, Marseille (Beyond
Uniform Hyperbolicity)
"Beyond Bowen's specification property"
(3 lectures). (Videos)
(Notes)
 April 13, 2019, University of Maryland
(Workshop
on dynamical systems and related topics)
"The measure of maximal entropy for geodesic
flows without conjugate points".
 July 17, 2018, RuhrUniversität Bochum.
"Unique equilibrium states for geodesic flows
in nonpositive curvature".
 June 22, 2018, ICMS, Edinburgh (Thermodynamic
formalism in dynamical systems)
"Leaf measures, dynamical dimensions, and
equilibrium states".
 April 17, 2018, University of
Massachussetts, Amherst.
"Unique equilibrium states for geodesic flows
in nonpositive curvature".
 October 6, 2017, Penn State (Workshop
in dynamical systems and related topics)
"Leaf measures via dynamical dimensions".
 August 4, 2017, University of British
Columbia (Current
trends in dynamical systems and the
mathematical legacy of Rufus Bowen)
"Unique equilibrium states for geodesic
flows in nonpositive curvature". (Slides)
 March 28, 2017, Trinity University, San
Antonio.
"Stochastic behavior in deterministic
dynamics". (Slides)
 March 20, 2017, Penn State.
"Young towers for surface
diffeomorphisms".
 February 2024, 2017, CIRM, Marseille (Nonuniformly
hyperbolic dynamical systems: coupling
and renewal theory)
"Young towers for surface
diffeomorphisms".
 February 3, 2017, UH Grad Student Seminar.
"Stochastic behavior in deterministic
dynamics". (Slides)
 January 6, 2017, Joint Mathematics
Meetings, Atlanta (AMS
special session on Ergodic Theory and
Dynamical Systems)
"Specification and Markov properties in shift
spaces".
 December 1, 2016, Australian National
University (Advances
in Ergodic Theory, Hyperbolic Dynamics &
Statistical Laws)
"Specification and Markov properties in shift
spaces". (Slides)
 October 29, 2016, Penn State (Workshop
in dynamical systems and related topics)
"A direct proof of the entropy gap for
rank 1 manifolds".
 October 9, 2016, University of Denver (AMS
Western Sectional Meeting: Special session on
zero dimensional dynamics)
"Specification and Markov properties in shift
spaces". (Slides)
 September 7, 2016, Sam Houston State
University colloquium.
"Stochastic behavior in deterministic
dynamics". (Slides)
 July 8, 2016, ICTP, Trieste, Italy.
"Equilibrium states for geodesic flow in
nonpositive curvature".
(School
on algebraic, geometric and probabilistic
aspect of dynamical systems and control theory)
 April 2529, 2016, ESI, Vienna.
"Equilibrium states for geodesic flow in
nonpositive curvature".
(Thermodynamic
formalism and mixing)
 March 711, 2016, ICERM, Brown University.
"Nonuniform specification properties,
thermodynamic formalism, and towers".
(Fractal
geometry, hyperbolic dynamics, and
thermodynamical formalism)
 January 12, 2016, Northwestern University.
"SRB measures and Young towers for surface
diffeomorphisms".
 January 11, 2016, University of Chicago.
"SRB measures and Young towers for
surface diffeomorphisms".
 October 23, 2015, Penn State.
(Workshop
in Dynamical Systems and Related Topics)
"Unique equilibrium states for geodesic flow
in nonpositive curvature".
 June 1013, 2015, Porto, Portugal.
(AMSEMSSPM
International Meeting: Special session on
recurrence, mixing, and fluctuations: statistics
of dynamical systems)
"Specification, statistical properties, and
towers".
 June 2, 2015, ICTP, Trieste, Italy.
"Effective hyperbolicity and SRB measures".
 May 18, 2015, University of Alabama at
Birmingham. (Conference
in memory of Nikolai Chernov)
"Specification, statistical properties, and
towers".
 May 7, 2015, University of Maryland.
"Unique equilibrium states for geodesic
flow in nonpositive curvature".
 April 30, 2015. University of
Mississippi.
"Thermodynamic formalism and uniform
mixing properties".
 March 14, 2015, Michigan State University.
(AMS
Central Sectional Meeting: Special session on
smooth dynamical systems and ergodic theory)
"Effective hyperbolicity and SRB measures".
(Slides)
 January 11, 2015, Joint Mathematics
Meetings, San Antonio. (AMS
special session on ergodic theory and
dynamical systems)
"Unique equilibrium states for some robustly
transitive systems". (Slides)
 September 15, 2014, University of Toronto.
"Equilibrium states, nonuniform mixing, and
towers"
 August 21, 2014, Ohio State University.
"Tower constructions from specification
properties"
 August 11, 2014, Banff, Alberta, Canada.
(Recent
Progress in Dynamical Systems and Related
Topics)
"Unique equilibrium states for some robustly
transitive systems". (Video)
 July 8, 2014, Madrid.
(AIMS
Conference on Dynamical Systems, Differential
Equations and Applications: Special
session on entropy and statistical properties
for smooth dynamics)
"Tower constructions and specification properties".
(Slides)
 June 2, 2014, University of North Texas.
(Logic
and Dynamics)
"Specification, hyperbolicity, and towers".
 May 30, 2014, UFRJ, Rio de Janeiro.
(Probability
in Dynamics)
"Specification, hyperbolicity, and towers".
(Notes)
 May 1422, 2014, University of Houston.
Multiple talks as part of UH
Summer School in Dynamical Systems.
 April 12, 2014, University of Maryland.
(Workshop
on Dynamical Systems and Related Topics)
"Tower constructions and specification properties".
(Notes)
 December 2, 2013, CIRM, Marseilles.
(Hyperbolicity
and dimension)
"Nonuniform specification, thermodynamic
formalism, and towers". (Slides)
 October 31, 2013, Indiana University,
Bloomington.
"SRB measures, unstable manifolds, and
effective hyperbolicity".
 October 28, 2013, University of Houston
(Dynamics seminar).
"SRB measures, unstable manifolds, and
effective hyperbolicity".
 October 8, 2013, Texas Christian University
(Colloquium).
"Thermodynamic formalism for dynamical
systems". (Slides)
 September 12, 2013, Ohio State University.
"SRB measures, unstable manifolds, and
effective hyperbolicity". (Notes)
 August 8, 2013, Guanajuato, Mexico.
(Mathematical
Congress of the Americas: Special Session on
Symbolic Dynamics).
"Large deviations using nonuniform
specification properties". (Slides)
 July 11, 2013, Pontificia Universidad
Católica de Chile, Santiago.
(Thermodynamic
formalism and applications).
"Thermodynamics for discontinuous maps and
potentials". (Slides)
 May 1321, 2013, University of Houston.
Multiple talks as part of UH
Summer School in Dynamical Systems.
 April 14,
2013, University of Colorado, Boulder.
(AMS
Western Sectional Meeting: Special Session on
Dynamical Systems: Thermodynamic formalism and
connections with geometry).
"Large deviations and nonuniform
specification properties". (Slides)
 April 10, 2013, University of Houston
(Undergraduate Colloquium).
"The bigness of things". (Slides)
 April 8, 2013, University of Houston
(Dynamics seminar).
"Large deviations in dynamical systems".
 March 20, 2013, EPFLCIB, Lausanne.
(Workshop on Large
deviations and thermodynamical formalism).
"Nonuniform specification properties and
large deviations". (Slides)
 March 3,
2013, University of Mississippi.
(AMS
Southeastern Sectional Meeting: Special
Session on Dynamical Systems).
"Effective
hyperbolicity and applications of new
HadamardPerron theorems". (Slides)
 February 25, 2013, University of Houston.
"The structure of the space of invariant
measures". (Notes)
 November 2, 2012, Rice University.
"Sarig's construction of countable Markov
partitions using Pesin theory".
(Notes)
 October 16, 2012, University of Houston (Pi
Mu Epsilon).
"Motivating examples in dynamical systems".
(Slides)
 October 5, 2012, University of Houston
(Graduate student seminar).
"Randomness and determinism in dynamical
systems". (Slides)
 February 20,
2012, Penn State.
"The structure
of the space of ergodic measures".
 February 7,
2012, University of Houston.
"Nonuniform
mechanisms for stochastic behaviour in
deterministic systems". (Slides)
 January 6,
2012, Joint Mathematics Meetings, Boston.
(Special
Session
on
Uniformly
and
Partially Hyperbolic Dynamical Systems).
"Unique
equilibrium states using regular collections
of times". (Slides)
 November 29,
2011, Brigham Young University.
"Usable
hyperbolicity and SRB measures".
(Slides)
 November 15,
2011, Northwestern University.
"Thermodynamics
with small obstructions". (Slides)
 October 31,
2011, University of Toronto.
"Thermodynamics
with small obstructions". (Slides)
 October 22,
2011, Penn State.
(Workshop
in Dynamical Systems and Related Topics).
"Unique
equilibrium states in nonuniform settings".
(Slides)
 August 12,
2011, GeorgAugustUniversität, Göttingen.
(Summer
School on Dynamical Systems).
"Usable
hyperbolicity and SRB measures".
(Slides)
 June 15,
2011, Centre de Physique Théorique,
Marseilles.
"SRB measures
without symbolic dynamics or dominated
splittings". (Slides)
 June 9, 2011,
CIRM, Marseilles.
(Beyond Uniform
Hyperbolicity 2011).
"SRB measures
without symbolic dynamics or dominated
splittings". (Slides)
 May 16, 2011,
Northwestern University.
"SRB measures
without symbolic dynamics or dominated
splittings". (Slides)
 May 3, 2011,
University of Illinois at UrbanaChampaign.
"Hölder
continuous potentials on betashifts have
unique equilibrium states". (Slides)
 April 21,
2011, Fields Institute.
"Multifractal
analysis via thermodynamics". (Slides)
 March 17,
2011, Penn State.
"The bigness
of things". (Notes)
 January 19,
2011, Penn State.
"Thermodynamics
for nonuniformly mixing systems:
factors of betashifts are intrinsically
ergodic". (Slides)
 November 11,
2010, University of Maryland.
"Thermodynamics
for nonuniformly mixing systems:
factors of betashifts are intrinsically
ergodic". (Slides)
 November 6,
2010, University of Richmond.
(AMS
Southeastern
Sectional
Meeting:
Special
Session
on
Statistical
Properties
of
Dynamical
Systems).
"SRB measures
for nonuniformly hyperbolic systems".
(Slides)
 October 21,
2010, Penn State.
(Workshop
in Dynamical Systems and Related Topics).
"SRB measures
for nonuniformly hyperbolic systems".
(Slides)
 April 11,
2010, University of Maryland.
(Workshop
on
Dynamical
Systems and Related Topics).
"Multifractal
analysis of Birkhoff averages". (Slides)
 February 23,
March 2 & 16, 2010, Penn State.
"Thermodynamic
formalism". (Notes)
 February 22,
2010, Penn State.
"Multifractals,
dimension
theory, and thermodynamics for general
dynamical systems". (Notes)
 November 1,
2009, Penn State.
(Workshop
in Dynamical Systems and Related Topics).
"A nonuniform
Bowen's equation and connections to
multifractal analysis". (Slides)
 August 21,
2009, IMERL, Montevideo.
"Bowen's
equation and multifractal analysis".
(Notes)
 July 21,
2009, GeorgAugustUniversität, Göttingen.
(Summer
School on Dynamical Systems).
"Dimension
theory, thermodynamics, and multifractals".
(Notes)
 May 22, 2009,
University of North Texas.
(Dynamical
Systems II).
"Blackbox
multifractal formalism". (Slides)
 April 5,
2009, University of Maryland.
(Conference
on
Dynamical
Systems and Related Topics).
"Blackbox
multifractal formalism". (Slides)
 September 16
& 23, 2008, Penn State.
"Measure
theory through dynamical eyes".



2020 Houston
Workshop on Hyperbolic Dynamical Systems
2017
Mathematics Research Communities at Snowbird, Utah
2019
Houston Summer School on Dynamical Systems
Selected expository blog posts (from seminar lectures
in preparation for our 2013 summer school)
Spectral methods in dynamics
Markov chains and mixing times
 Part 1
(Feb. 11 lecture by Matt Nicol)
 Part 2
(Feb. 18 lecture by Matt Nicol)
 Part 3
(Feb. 25 lecture by Matt Nicol)
Convex cones and the Hilbert metric
Martingale methods
