Research
For recent publications please see
this
Google Scholar link. Publications related to data assimilation
are also on the
UMD Weather
& Chaos publication page.
Below is mainly an index through 2005 to my journal articles, and a few
papers from conference proceedings, organized into several themes.
In most cases, the last line of a reference is a link to a journal
web site with the abstract (and link to full text) for the paper, or
in some cases a link straight the full text. Access to the full text
requires a subscription for some journals. For a few papers, the
title is a link to a preprint version. For others, you may be able to
find preprint versions via Google
Scholar.
Sections:
These papers discuss mathematical applications to weather forecasting
models and other highdimensionals dynamical systems. Many are
concerned with the problem of state estimation: determining the
most likely state of a system, given a model for the system and
limited observations made over a period of time.
Click
here for preprints and related publications.

I. Szunyogh, E. Kostelich, G. Gyarmati, D. Patil, B. Hunt, E. Kalnay,
E. Ott and J. Yorke,
Assessing a local ensemble Kalman filter: perfect model experiments
with the NCEP global model,
Tellus A 57 (2005), 528545.

J. Harlim, M. Oczkowski, J. Yorke, E. Kalnay, B. Hunt,
Convex error growth patterns in a global weather model,
Phys. Rev. Lett. 94 (2005), 228501 (4 pages).

S.J. Baek, B. Hunt, I. Szunyogh, A. Zimin, E. Ott,
Localized error bursts in estimating the state of spatiotemporal
chaos,
Chaos 14 (2004), 10421049.

E. Ott, B. Hunt, I. Szunyogh, A. Zimin, E. Kostelich,
M. Corazza, E. Kalnay, D. Patil, J. Yorke,
A local ensemble Kalman filter for atmospheric data assimilation,
Tellus A 56 (2004), 415428.

E. Ott, B. Hunt, I. Szunyogh, A. Zimin, E. Kostelich,
M. Corazza, E. Kalnay, D. Patil, J. Yorke,
Estimating the state of large spatiotemporally chaotic systems,
Phys. Lett. A 330 (2004), 365370.

B. Hunt, E. Kalnay, E. Kostelich, E. Ott, D. Patil, T. Sauer,
I. Szunyogh, J. Yorke, A. Zimin,
Fourdimensional ensemble Kalman filtering,
Tellus A 56 (2004), 273277.

M. Corazza, E. Kalnay, D. Patil, S.C. Yang, R. Morss, M. Cai,
I. Szunyogh, B. Hunt, J. Yorke,
Use of the breeding technique to estimate the structure of the
analysis ``errors of the day'',
Nonlin. Process. Geophys. 10 (2003), 233243.

A. Zimin, I. Szunyogh, D. Patil, B. Hunt, E. Ott,
Extracting envelopes of Rossby wave packets,
Monthly Weather Rev. 131 (2003), 847953.

D. Patil, B. Hunt, E. Kalnay, J. Yorke, E. Ott,
Local low dimensionality of atmospheric dynamics,
Phys. Rev. Lett. 86 (2001), 58785881.

D. Patil, B. Hunt, J. Carton,
Identifying low dimensional nonlinear behavior in atmospheric data,
Monthly Weather Rev. 129 (2001), 21162125.
These papers develop and apply the notion of "prevalence" to
describe what is measuretheoretically typical in a space
Some applications are to dynamics, and others are to describe the
effect that a typical "projection" has on a set or a measure
in a vector space, where by projection I mean a smooth (not
necessarily linear) mapping into a lower dimensional space.

V. Kaloshin & B. Hunt,
Stretched exponential estimate on the growth of the number of periodic
points for prevalent diffeomorphisms,
Ann. Math., in press.

W. Ott, B. Hunt, V. Kaloshin,
The effect of projections on fractal sets and measures in Banach
spaces,
Ergod. Th. Dynam. Sys., in press.

V. Kaloshin & B. Hunt,
A stretched exponential bound on the rate of growth of the number of
periodic points for prevalent diffeomorphisms I & II,
Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 1727;
Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 2836.

B. Hunt & V. Kaloshin,
Regularity of embeddings of infinitedimensional fractal sets into
finitedimensional spaces,
Nonlinearity 12 (1999), 12631275.

B. Hunt & V. Kaloshin,
How projections affect the dimension spectrum of fractal measures,
Nonlinearity 10 (1997), 10311046.

B. Hunt,
The prevalence of continuous nowhere differentiable functions,
Proc. Amer. Math. Soc. 122 (1994), 711717.

B. Hunt, T. Sauer, J. Yorke,
Prevalence: a translationinvariant ``almost every'' on
infinitedimensional spaces,
Bull. Amer. Math. Soc. 27 (1992), 217238;
Bull. Amer. Math. Soc. 28 (1993), 306307 (Addendum).
These papers consider fractal sets and measures that arise in
dynamical systems, and their characterization by various notions of
"dimension". Some of the papers in Prevalence also discuss properties of fractal
dimensions.

J.W. Kim, S.Y. Kim, B. Hunt, E. Ott,
Fractal properties of robust strange nonchaotic attractors in
maps of two or more dimensions,
Phys. Rev. E 67 (2003), 036211 (8 pages).

B. Hunt and E. Ott,
Fractal properties of robust strange nonchaotic attractors,
Phys. Rev. Lett. 87 (2001), 254101 (4 pages).

P. So, E. Barreto, B. Hunt,
Boxcounting dimension without boxes: computing D_{0} from
average expansion rates,
Phys. Rev. E 60 (1999), 378385.

B. Hunt, E. Ott, E. Rosa,
Sporadically fractal basin boundaries of chaotic systems,
Phys. Rev. Lett. 82 (1999), 35973600.

B. Hunt,
The Hausdorff dimension of graphs of Weierstrass functions,
Proc. Amer. Math. Soc. 126 (1998), 791800.
(Alternate link)

W. Chin, B. Hunt, J. Yorke,
Correlation dimension for iterated function systems,
Trans. Amer. Math. Soc. 349 (1997), 17831796.
(Alternate link)

B. Hunt, E. Ott, J. Yorke,
Fractal dimensions of chaotic saddles of dynamical systems,
Phys. Rev. E 54 (1996), 48194823.

B. Hunt, K. Khanin, Ya. Sinai, J. Yorke,
Fractal properties of critical invariant curves,
J. Stat. Phys. 85 (1996), 261276.

B. Hunt,
Maximum local Lyapunov dimension bounds the box dimension of chaotic
attractors,
Nonlinearity 9 (1996), 845852.

B. Hunt, I. Kan, J. Yorke,
When Cantor sets intersect thickly,
Trans. Amer. Math. Soc. 339 (1993), 869888.

B. Hunt & J. Yorke,
Smooth dynamics on Weierstrass nowhere differentiable curves,
Trans. Amer. Math. Soc. 325 (1991), 141154.
These papers involve invariant measures of chaotic dynamical systems.
Several of them develop and study the question of which orbit or
invariant measure of a chaotic system is "optimal", in the sense that
it maximizes the average of some realvalued function of the system
state.

D. Armstead, E. Ott, B. Hunt,
Powerlaw decay and selfsimilar distributions in stadiumtype billiards,
Physica D 193 (2004), 96127.

D. Armstead, B. Hunt, E. Ott,
Anomalous diffusion in infinite horizon billiards,
Phys. Rev. E 67 (2003), 021110 (7 pages).

D. Armstead, B. Hunt, E. Ott,
Long time algebraic relaxation in chaotic billiards,
Phys. Rev. Lett. 89 (2002), 284101 (4 pages).

B. Hunt, J. Kennedy, T.Y. Li, H. Nusse,
SLYRB measures: natural invariant measures for chaotic systems,
Physica D 170 (2002), 5071.

T.H. Yang, B. Hunt, E. Ott,
Optimal periodic orbits for continuous time systems,
Phys. Rev. E 62 (2000), 19501959.

G. Yuan & B. Hunt,
Optimal orbits of hyperbolic systems,
Nonlinearity 12 (1999), 12071224.

B. Hunt & E. Ott,
Optimal periodic orbits of chaotic systems occur at low period
Phys. Rev. E 54 (1996), 328337.

B. Hunt & E. Ott,
Optimal periodic orbits of chaotic systems,
Phys. Rev. Lett. 76 (1996), 22542257.

B. Hunt,
Estimating invariant measures and Lyapunov exponents,
Ergod. Th. Dynam. Sys. 16 (1996), 735749.
These papers consider models of network growth, the dynamics of
networks of coupled oscillators, and the dynamics of TCP networks.

R. Lance, I. Frommer, B. Hunt, E. Ott, J. A. Yorke, E. Harder,
Roundtrip time inference via passive monitoring,
Proc. of the Workshop on Large Scale Network Inference (LSNI):
Methods, Validation, and Applications, ACM SIGMETRICS (June 2005,
Banff, Alberta, Canada).

J. Restrepo, E. Ott, B. Hunt,
Onset of synchronization in large networks of coupled oscillators,
Phys. Rev. E 71 (2005), 036151 (12 pages).

I. Frommer, B. Hunt, R. Lance, E. Ott, J. A. Yorke, E. Harder,
Modeling congested Internet connections,
Proc. of the IASTED International Conference on Communications and
Computer Networks (November 2004, Cambridge, MA), pp. 319324.

J. Restrepo, E. Ott, B. Hunt,
Desynchronization waves and localized instabilities in oscillator
arrays,
Phys. Rev. Lett. 93 (2004), 114101 (4 pages).

J. Restrepo, E. Ott, B. Hunt,
Spatial patterns of desynchronization bursts in networks,
Phys. Rev. E 69 (2004), 066215 (11 pages).

J. Ozik, B. Hunt, E. Ott,
Growing networks with geographical attachment preference: emergence of
small worlds,
Phys. Rev. E 69 (2004), 026108 (5 pages).

J.W. Kim, B. Hunt, E. Ott,
Evolving networks with multispecies nodes and spread in the number of
initial links,
Phys. Rev. E 66 (2002), 046115 (5 pages).
These papers are concerned with the dynamics of systems with a
invariant manifold (possibly due to a symmetry). When the dynamics
within the invariant manifold are chaotic, the manifold often is only
partially stable, in the sense that in an arbitrarily small
neighborhood of the manifold, most trajectories are attracted to it
but some trajectories are repelled. If noise is added to the system,
the dynamics near the manifold may then be intermittent, with
trajectories spending most of their time near the manifold but
occasionally venturing far away. A scenario of particular interest is
when the invariant manifold consists of states in which two or more
coupled systems are behaving synchronously. The paper with Baek in
Weather Forecasting and the papers with
Restrepo under Dynamics on Networks also
discuss synchronization of coupled systems.

S.Y. Kim, W. Lim, E. Ott, B. Hunt,
Dynamical origin for the occurrence of asynchronous hyperchaos
and chaos via blowout bifurcations,
Phys. Rev. E 68 (2003), 066203 (10 pages).

A. Zimin, B. Hunt, E. Ott,
Bifurcation scenarios for the bubbling transition,
Phys. Rev. E 67 (2003), 016204 (13 pages).

B. Hunt, E. Ott, J. Yorke,
Differentiable generalized synchronization of chaotic systems,
Phys. Rev. E 55 (1997), 40294034.

S. Venkataramani, B. Hunt, E. Ott,
The bubbling transition
Phys. Rev. E 54 (1996), 13461360.

S. Venkataramani, B. Hunt, E. Ott, D. Gauthier, J. Bienfang,
Transitions to bubbling of chaotic systems
Phys. Rev. Lett. 77 (1996), 53615364.

J. Alexander, B. Hunt, I. Kan, J. Yorke,
Intermingled basins for the triangle map,
Ergod. Th. Dynam. Sys. 16 (1996), 651662.
These papers study the parameter dependence of dynamical systems,
considering both bifurcations at specific parameter values and the
interplay between stable periodicity and chaotic behavior in parameter
space as a whole. Several of the papers in Dynamics near Invariant Manifolds also are
concerned with bifurcations.

B. Hunt & T. Young,
Critical saddlenode bifurcations and MorseSmale maps,
Physica D 197 (2004), 117.

B. Hunt, J. Gallas, C. Grebogi, J. Yorke, H. Koçak,
Bifurcation rigidity,
Physica D 129 (1999), 3556.

J. Jacobs, E. Ott, B. Hunt,
Scaling of the durations of chaotic transients in windows of
attracting periodicity,
Phys. Rev. E 56 (1997), 65086515.

E. Barreto, B. Hunt, C. Grebogi, J. Yorke,
From high dimensional chaos to stable periodic orbits: the structure
of parameter space,
Phys. Rev. Lett. 78 (1997), 45614564.

B. Hunt & E. Ott,
Structure in the parameter dependence of order and chaos for the
quadratic map,
J. Phys. A 30 (1997), 70677076.

J. Jacobs, E. Ott, B. Hunt,
Calculating topological entropy for transient chaos with an
application to communicating with chaos,
Phys. Rev. E 57 (1998), 65776588.

U. Feudel, C. Grebogi, B. Hunt, J. Yorke,
A map with more than 100 coexisting lowperiod periodic attractors,
Phys. Rev. E 54 (1996), 7181.

B. Hunt & J. Yorke,
Maxwell on chaos,
Nonlin. Sci. Today 3 (1993), 14.

B. Hunt & J. Yorke,
When all solutions of x' = Σ q_{i}(t) x(t 
T_{i}(t)) oscillate,
J. Diff. Eq. 53 (1984), 139145.

M. Roberts, W. Hayes, B. Hunt, S. Mount, J. Yorke,
Reducing storage requirements for biological sequence comparison,
Bioinformatics 20 (2004), 33633369.

M. Roberts, B. Hunt, J. Yorke, R. Bolanos, A. Delcher,
A preprocessor for shotgun assembly of large genomes,
J. Comp. Bio. 11 (2004), 734752.

S. Guharay, B. Hunt, J. Yorke, O. White,
Correlations in DNA sequences across the three domains of life,
Physica D 146 (2000), 388396.
Back to my home page.
Updated: August 2005