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PROFESSOR MIKE FIELD
Marie Curie Fellow
Phone: +44(207)5941424
Room: 620 Huxley Building


Areas of Interest
 Asynchronous networks and event driven dynamics. Applications to engineering (esp. power and microgrids), neuroscience and learning.
 Ergodic theory and mixing; statistical properties of dynamical systems.
 Geometric theory of dynamical systems with symmetry; bircation theory; heteroclinic cycles and networks.
 Dynamics of coupled cell systems and heteroclinic cycles.
 Visualization of complex dynamics; mathematical education.
For more details, see my personal web pages at Imperial or at UC Santa Barbara.
Grants (from 1994), Awards and Honours
 Continuous NSF funding since 1994; funding from Texas Advanced Research Program, Office of Naval Research; LMS and EPSRC
 Fellow of the Institute of Physics (2004)
 Visiting Leverhulme Professorship, Imperial College (20042005)
 Visiting Ulam Professor, Boulder (2005)
 Gaines Scholar, University of Richmond (2006)
 Honorary Visiting Professor, Exeter University (from 2009)
 Inaugural AMS Fellow (2012)
 On Fulbright Specialist Roster (from 2013)
 Marie Curie International Fellow, 20142016.
Publications
Books and Monographs  since 1996
 M J Field. Symmetry breaking for compact Lie groups,
Memoirs of the American Mathematical Society, 574, 1996.
 M J Field. Lectures on Bifurcations, Dynamics and Symmetry,
Pitman Research Notes in Mathematics, 356, 1996.
 M J Field and M Nicol,
Ergodic Theory of
equivariant diffeomorphisms: Markov partitions and Stable Ergodicity, Memoirs AMS,
169, 2004.
 M J Field. Dynamics and Symmetry, (Imperial College Press, Advanced texts in mathematics, Vol. 3, 2007)
 M J Field and M Golubitsky. Symmetry in Chaos (2nd edition),
SIAM, May 22, 2009
 M J Field. Differential Calculus and its Applications. Dover, 2012.
 M J Field. Essential Real Analysis Undergraduate/graduate level text (SpringerSUMS series, 2017).
A selection of recent journal articles
 M Aguiar, A Dias and M J Field, Feedforward Networks: Adaptation, Feedback, and Synchrony, Journal of Nonlinear Science, November, 2018.
 C Bick and M J Field, Asynchronous Networks and Event Driven Dynamics, Nonlinearity 30(2) (2017).
 C Bick and M J Field, Asynchronous Networks: Modularization of dynamics theorem, Nonlinearity 30(2) (2017) .
 C Bick and M J Field, Asynchronous Networks, to appear in Springer special issue of Research Perspectives CRM Barcelona: Nonsmooth Dynamics.
 C Bick and M J Field, Asynchronous Networks: Factorization of Dynamics and Function, MATEC Web of Conferences, 83 (2016).
 M J Field, Patterns of Desynchronization and Resychronization in Heteroclinic Networks, Nonlinearity 30(2) (2017).
 M J Field, Heteroclinic networks in homogeneous and heterogeneous identical cell systems, Journal of Nonlinear Science
25(3) (2015), 779813.
 N Agarwal, A Rodrigues and M J Field,
Dynamics near the Product of Planar Heteroclinic Attractors,
Dynamical Systems: An International Journal, 26(4) (2011), 447481.
 M Aguiar, P Ashwin, A Dias, and M J Field,
Dynamics of coupled cell systems: synchrony, heteroclinic cycles and inflation, Journal of Nonlinear Science,
21(2) (2011), 271323.
 M J Field, Exponential mixing for smooth hyperbolic suspension flows, Regular and Chaotic Dynamics 16(12) (2011), 90103.
 N Agarwal and M J Field,
Dynamical equivalence of network architecture for coupled dynamical systems II: general case, Nonlinearity 23 (2010), 12691289.
 N Agarwal and M J Field, Dynamical equivalence of network architecture for coupled dynamical systems I: asymmetric inputs,
Nonlinearity 23 (2010), 12451268.
 M J Field, Singularity and stratification theory applied to dynamical systems,
Singularity Theory, Proceedings of the 2005 Marseille Singularity School and Conference, WSC, (2007), 219240.
 M J Field, I Melbourne and A Torok. Stability of rapid mixing for hyperbolic flows,
Annals of Mathematics, 166(1) (2007), 269291.
 M J Field, I Melbourne and A Torok.
Stable
ergodicity for smooth compact Lie group extensions of hyperbolic basic
sets.
, Ergodic Theory & Dynamical Systems, 25 (2) (2005), 517551.
 P Ashwin and M Field
Product dynamics for homoclinic attractors
, Proc. Royal Soc., Ser. A, 461 (2005), 155177.
 M J Field.
Combinatorial Dynamics, Dynamical Systems, 19 (2004), 217243.
 M J Field, I Melbourne and A Torok. Decay of Correlations, Central Limit Theorems
and Approximation by
Brownian Motion for Compact Lie Group Extensions, Ergodic Theory & Dynamical Systems,
2003.
 P Ashwin and M J Field, Heteroclinic networks in coupled cell systems,
Arch. Rat. Mech. and Anal., 148 (1999), 107143.
 M J Field, Generating sets for compact
semisimple Lie groups, Proc. AMS, 127(11) (1999), 33613365.
 M J Field and W Parry, Stable ergodicity of skew extensions by compact
Lie groups, Topology 38(1), (1999), 167187.
 M J Field. Symmetry breaking for equivariant maps,
In: Algebraic groups and Lie groups, Volume in
Honour of R W Richardson, Cambridge University Press,
(1997), 219253.
 M J Field, I Melbourne and M Nicol. Symmetric
attractors for diffeomorphisms and flows,
Proc. London Math. Soc. 72 (1996), 657696.
