Mike Field – Dynamical Systems at Imperial College London (DynamIC)

Asynchronous networks and event driven dynamics. Applications to engineering, 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.

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 (2004--2005)\\
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 (2013)
Marie Curie International Fellow, 2014-2016.

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

A selection of recent journal articles

C Bick and M J Field, Asynchronous Networks and Event Driven Dynamics, preprint (2015).
M J Field, Heteroclinic networks in homogeneous and heterogeneous identical cell systems, Journal of Nonlinear Science

N Agarwal, A Rodrigues and M J Field, Dynamics near the Product of Planar Heteroclinic Attractors, Dynamical Systems: An International Journal, 26(4) (2011), 447-481.
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), 271-323.
M J Field, Exponential mixing for smooth hyperbolic suspension flows, Regular and Chaotic Dynamics 16(1-2) (2011), 90-103.

N Agarwal and M J Field, Dynamical equivalence of network architecture for coupled dynamical systems II: general case, Nonlinearity 23 (2010), 1269-1289.

N Agarwal and M J Field, Dynamical equivalence of network architecture for coupled dynamical systems I: asymmetric inputs, Nonlinearity 23 (2010), 1245-1268.

M J Field, Singularity and stratification theory applied to dynamical systems, Singularity Theory, Proceedings of the 2005 Marseille Singularity School and Conference, WSC, (2007), 219-240.

M J Field, I Melbourne and A Torok. Stability of rapid mixing for hyperbolic flows, Annals of Mathematics, 166(1) (2007), 269-291.

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), 517-551.

P Ashwin and M Field Product dynamics for homoclinic attractors , Proc. Royal Soc., Ser. A, 461 (2005), 155-177.

M J Field. Combinatorial Dynamics, Dynamical Systems, 19 (2004), 217-243.

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), 107-143.

M J Field, Generating sets for compact semisimple Lie groups, Proc. AMS, 127(11) (1999), 3361-3365.

M J Field and W Parry, Stable ergodicity of skew extensions by compact Lie groups, Topology 38(1), (1999), 167-187.

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), 219-253.

M J Field, I Melbourne and M Nicol. Symmetric attractors for diffeomorphisms and flows, Proc. London Math. Soc. 72 (1996), 657-696.