- 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, I Melbourne and M Nicol. Symmetric
attractors for diffeomorphisms and flows,
Proc. London Math. Soc. 72 (1996), 657-696.
- 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. (PDF file)
- M J Field and W Parry, Stable ergodicity of skew extensions by compact
Lie groups, Topology 38(1), (1999), 167-187.
- M J Field, Generating sets for compact
semisimple Lie groups, Proc. AMS, 127(11) (1999), 3361-3365.
- P Ashwin and M J Field, Heteroclinic networks in coupled cell systems,
Arch. Rat. Mech. and Anal., 148 (1999), 107-143. ( PDF)
- M J Field and V Nitica, Stable topological transitivity
of skew and principal extensions, Nonlinearity 14 (2001), 1055-1070.
- 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. (PDF file of article.)
- P Ashwin, M Field, A M Rucklidge and R Struman.
Phase resetting effects for robust cycles between chaotic sets,
Chaos 13 (2003), 973-981, focus issue on chaotic itineracy.
- M J Field.
Combinatorial Dynamics, Dynamical Systems, 19 (2004), 217-243.
(PDF file - version of May 25, 2004).
- M J Field and M Nicol,
Ergodic Theory of
equivariant diffeomorphisms: Markov partitions and Stable Ergodicity, Memoirs AMS,
169, 2004.
(PS file of article).
- P Ashwin and M Field
Product dynamics for homoclinic attractors
, Proc. Royal Soc., Ser. A, 461 (2005), 155-177. PDF file (version of May 2004).
- 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.
Preprint PDF file
of article.
- M J Field, I Melbourne, M Nicol and A Torok. Statistical properties of compact
group extensions of hyperbolic flows and their time one maps, Discrete and Continuous Dynamical Systems, 2 (1) (2005), 79-96.
Preprint PDF file of article.
- M J Field, I Melbourne and A Torok. Stability of rapid mixing for hyperbolic flows,
Annals of Mathematics, 166(1) (2007), 269-291. PDF file (version of 2005).
- 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. Preprint PDF file of article.
- M J Field, Dynamics and Symmetry, (Imperial College Press, Advanced texts in mathematics, Vol. 3, 2007, PDF file of preface and
table of contents.)
- N Agarwal and M J Field, Dynamical equivalence of network architecture for coupled dynamical systems I: asymmetric inputs,
preprint 2010, Nonlinearity 23 (2010), 1245-1268.
- N Agarwal and M J Field,
Dynamical equivalence of network architecture for coupled dynamical systems II: general case, preprint 2010, Nonlinearity 23 (2010), 1269-1289.
- 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
(preprint July 2011).
- M J Field, Exponential mixing for smooth hyperbolic suspension flows, Regular and Chaotic Dynamics 16(1-2) (2011), 90-103.
(preprint 2010, version of Oct, 2010.)
- 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. (preprint 2010, version of August, 2010).
- M J Field, Heteroclinic networks in homogeneous and heterogeneous identical cell systems, Journal of Nonlinear Science, 25(3) (2015), 779-813. (preprint, version of Jan 11, 2015)
- C Bick and M J Field, Functional Asynchronous Networks:
Factorization of Dynamics and Function, (preprint 2016), MATEC Web of Conferences, 83 (2016).
- Christian Bick and Michael Field, Asynchronous Networks and Event Driven Dynamics, (preprint 2016, Updated May 10, 2016), Nolinearity 30(2) (2017), 558-594.
- C Bick and M J Field, Asynchronous Networks: Modularization of Dynamics Theorem, (preprint 2016, May 10, 2016), Nolinearity 30(2) (2017), 595-621.
- M J Field, Patterns of Desynchronization and Resychronization in Heteroclinic Networks,
Nonlinearity 30(2) (2017), 516-557 (preprint, updated version of November 16, 2016)
- C Bick and M J Field, Asynchronous Networks, (preprint May 2016),
Springer special issue Research Perspectives CRM Barcelona: Nonsmooth Dynamics,
- M A D Aguiar, A P Dias, and M J Field, Feedforward Networks: Adaptation, Feedback, and Synchrony,
J. Nonlinear Sci., November, 2018 (Version of September, 2018,
Initialization data for examples.)
- Y Arjevani and M J Field, On the principle of least symmetry breaking in shallow relu Models, arXiv preprint arXiv:1912.11939, 2019.
- Y Arjevani and M J Field, Analytic Characterization of the Hessian in Shallow ReLu Models: A Tale of Symmetry, Proc. Neurips 2020 (arXiv preprint arXiv:2008.01805).
- Y Arjevani and M J Field, Symmetry and critical points for a model shallow neural network, Physica D, 427 (December, 2021),
arXiv preprint arXiv:2003.10576, 2020. (zipped file of critical point data for spurious minima of types I, II and A) .
- Y Arjevani, J Bruna, M J Field, J Kileel, M Trager, and F Williams. Symmetry Breaking in Symmetric Tensor Decomposition,
arXiv preprint arXiv:2103.06234, 2021.
- Y Arjevani and M J Field, Equivariant bifurcation, quadratic equivariants, and symmetry breaking for the standard representation of Sn, Nonlinearity 35 (2022), 2809-2857 (arXiv preprint arXiv:2107.02422, 2021).
- Y Arjevani and M J Field, Analytic Study of Families of Spurious Minima in Two-Layer ReLU Neural Networks: A Tale of Symmetry II, Proc. Neurips 2021 (arXiv preprint arXiv:2107.10370, 2021).
- Y Arjevani and M J Field, Annihilation of Spurious Minima in Two-Layer ReLU Networks, Proc. Neurips 2022, to appear, (arXiv preprint arXiv:2210.06088, 2022).
Art and Mathematics
- M J Field Bridges London, 2006, Notices of the AMS, 54(6) (2007), 730--732.
email: mikefield@gmail.com
Professor Mike Field
Department of Mechanical Engineering
University of California
Santa Barbara, CA 93106
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