H. Scott Dumas

Research Interests:  Dynamical systems and applied mathematics, with emphasis on both theory and applications of averaging methods for ordinary differential equations, ergodic theory, Hamiltonian perturbation theory, and kinetic theory.  Applied work extends into these areas of physics: condensed matter-particle interactions, beam stability and spin-orbit interactions in particle accelerators, celestial mechanics, and gas dynamics.
 

1982 -2025 More than twenty visiting positions at universities, laboratories and research institutes in the U.S., France, Germany, Brazil, and China.,

1995 -1998 NSF Principal Investigatorship (DMS/Geometric Analysis)

1993 -1999 Ohio Supercomputer Center Award

1992 -1994 NSF Principal Investigatorship (DMS/Applied Mathematics)

1991 -2013 University of Cincinnati C.P. Taft Travel, Research, and Publication Grants

1989 -1990 IMA Postdoctoral Membership, University of Minnesota-Twin Cities

1986 -1987 American Fulbright Advanced Student Award (Host institution: ENS-Paris)

Book

See also H.S. Dumas’ Amazon Author Page for more information about these books, as well as other books containing some of the articles listed above.

Dumas, H.S. [translated by Jian Chen] The KAM Story, Higher Education Press, Beijing, 2021
[Chinese translation of The KAM Story, above]

Dumas, H.S. [Translated by V.V. Shulikovskaya, with Scientific Editors I.V. Bizyaev and A.V. Borisov].  Teoriya KAM: kak eto bylo (Kratkoe znakomstvo s soderzhaniem, istoriey i znacheniem klassicheskoy teorii Kolmogorova-Arnolda-Mozera), Regulyarnaya i haoticheskaya dinamika, Institut kompyuternyh issledovaniy, Moskva, 2017
[Russian translation of The KAM Story, above].

Dumas, H.S.  The KAM Story: a friendly introduction to the content, history, and significance of classical Kolmogorov-Arnold-Moser theory, World Scientific Publishers, Singapore, 2014
[Russian and Chinese translations see below].

Dumas, H.S., Meyer, K.R. & Schmidt, D.S., Eds.  Hamiltonian Dynamical Systems: History, Theory, and Applications (IMA Volumes in Mathematics and its Applications, Vol. 63), Springer-Verlag, New York, 1995.

Lochak, P. & Meunier, C. [Translated by H.S. Dumas].  Multiphase Averaging for Classical Systems with Applications to Adiabatic Theorems (Applied Mathematical Sciences Vol. 72), Springer-Verlag, New York, 1988.

Translations

Albouy, A. & Bennequin, D. [Translated by H.S. Dumas] (2023). Preface to Special Issue Dedicated to Alain Chenciner. Regular and Chaotic Dynamics, 28, Nos. 4-5: 338-341.

Albouy, A. [Translated by H.S. Dumas] (2002).  Lectures on the two-body problem, in Classical and Celestial Mechanics: The Recife Lectures (H. Cabral and F. Diacu, Eds.) 63–116, Princeton University Press, Princeton, NJ.

Albouy, A. [Translated by H.S. Dumas] (1993).  Integral manifolds of the N-body problem.  Inventiones Mathematicae 114: 463--488.

Merle, F.  [Translated by H.S. Dumas] (1988).  Existence of stationary states for nonlinear Dirac equations.  Journal of Differential Equations 74: 50–68.

Peer Reviewed Publications

Dumas, H.S. & Fischler, S. (2022).  Filling times for linear flow on the torus with truncated Diophantine conditions: a brief review and new proof. Qualitative Theory of Dynamical Systems  21, 103 [15 pages].

Dumas, H.S., Meyer, K.R., Palacian, J.F., & Yanguas, P.  (2017).  Asymptotic stability estimates near an equilibrium point.  Journal of Differential Equations  263, 1125–1139.

Dumas, H.S. (2013).  A specialized multiphase averaging method for quasiperiodic systems of ODEs.  Qualitative Theory of Dynamical Systems 12 (1) 225–242. 

Graça, D.S., Zhong, N., & Dumas, H.S. (2012). The connection between computability of a nonlinear problem and its linearization: the Hartman-Grobman theorem revisited.  Theoretical Computer Science 457, 101–110.

Dumas, H.S., Meyer, K.R., Palacián, J., & Yanguas, P. (2007).  Qualitative features of Hamiltonian systems through averaging and reduction, in Actas del XX Congreso de Ecuaciones Diferenciales y Aplicaciones, X Congreso de Matemática Aplicada (held in Sevilla, Spain, September 24–28, 2007), 8 pp., Sociedad Española de Matemática Aplicada, Universidad de Sevilla.

Dumas, H.S., & Ellison, J.A. (2005). Averaging for Quasiperiodic Systems. in Equadiff 2003: Proceedings of the International Conference on Differential Equations, Hasselt, Belgium (F. Dumortier, H.W. Broer, J. Mawhin, A. Vanderbauwhede, & S. Verduyn Lunel, Eds.), World Scientific, Singapore, 2005, pp. 726–731.

Dumas, H.S., Ellison, J.A., & Vogt, M. (2004).  First-order averaging principles for maps with applications to accelerator beam dynamics. SIAM Journal on Applied Dynamical Systems, 3 (4), 409–432.

Dumas, H.S., Ellison, J.A., Salas, M., Sen, T., Sobol, A., & Vogt, M. (2003). Weak-strong beam-beam: averaging and tune diagrams. Beam Halo Dynamics, Diagnostics, and Collimation: 29th ICFA Advanced Beam Dynamics Workshop on Beam-Halo Dynamics and the Beam-Beam Interaction, pp. 282–286.

Dumas, H.S., Ellison, J.A., & Hoffstaetter, G. (2002).  Adiabatic invariants for spin-orbit motion. in Proceedings of the Eighth European Particle Accelerator Conference (Paris, France, June 3–7, 2002) EPS-IGA & CERN, Geneva, 2002, pp. 332–334.

Dumas, H.S., Ellison, J.A., & Golse, F. (2000). A mathematical theory of planar particle channeling in crystals. Physica D 146 (1–4), 341–366.

Dumas, H.S. (1999).  Filling rates for linear flow on the torus: recent progress and applications, in Hamiltonian Systems with Three or More Degrees of Freedom (C. Simó, Ed.), 335–339, Kluwer Academic Publishers, Dordrecht.

Dumas, H.S. (1998).  Mathematical aspects of high-energy particle motion in periodic structures, in Nonlinear and Stochastic Beam Dynamics in Accelerators – A Challenge to Theoretical and Computational Physics (A. Bazzani, J.A. Ellison, H. Mais, G. Turchetti, Eds.), 140–160, DESY, Hamburg.

Dumas, H.S., Dumas, L. & Golse, F. (1997).  Remarks on the notion of mean free path for a periodic array of spherical obstacles.  Journal of Statistical Physics 87 (3/4): 943–950.

Dumas, H.S. & Golse, F. (1997).  The averaging method for perturbations of mixing flows.  Ergodic Theory and Dynamical Systems 17: 1339–1358.

Dumas, H.S., Dumas, L. & Golse, F.  (1996).  On the mean free path for a periodic array of spherical obstacles.  Journal of Statistical Physics 82 (5/6): 1385–1407.

Dumas, H.S.  (1995).  A new proof of Anosov`s averaging theorem, in Hamiltonian Dynamical Systems:  History, Theory, and Applications  (H.S. Dumas, K.R. Meyer, D. Schmidt, Eds.),  IMA Volumes in Mathematics and its Applications 63: 127–136, Springer-Verlag, New York.

Yanguas, P., Palacián, J., Meyer, K.R., & Dumas, H.S. (2008).  Periodic solutions in Hamiltonian systems, averaging, and the lunar problem. SIAM Journal on Applied Dynamical Systems 7 (2): 311–340.

Dumas, H.S., Ellison, J.A., & Hoffstaetter, G. (2006). Adiabatic invariance of spin-orbit motion in accelerators. Physical Review ST - Accelerators and Beams, 9 (1): 014001 [13 pp].

Dumas, H.S. (2005).  Mathematical theories of classical particle channeling in perfect crystals. NIM Physics Research Section B: Beam Interactions with Materials and Atoms 234 (1–2), 3–13.

Dumas, H.S., Golse, F. & Lochak, P.  (1994).  Multiphase averaging for generalized flows on manifolds.  Ergodic Theory and Dynamical Systems 14: 53–68.

Dumas, H.S. & Laskar, J.  (1993).  Global dynamics and long-time stability in Hamiltonian systems via numerical frequency analysis.  Physical Review Letters 70 (20): 2975–2979.

Dumas, H.S. (1993).  A Nekhoroshev-like theory of classical particle channeling in perfect crystals.  Dynamics Reported (New Series) 2: 69–115.

Dumas, H.S. & Ellison, J.A.  (1991).  Nekhoroshev's theorem, ergodicity, and the motion of energetic charged particles in crystals, in Essays on Quantum and Classical Dynamics (J.A. Ellison and H. Überall, Eds.): 17–56, Gordon and Breach, Philadelphia.

Dumas, H.S.  (1991).  Existence and stability of particle channeling in crystals on timescales beyond all orders, in Asymptotics Beyond All Orders (H. Segur, S. Tanveer, and H. Levine, Eds.)  NATO ASI Series B: Physics 284: 267–273, Plenum Press, New York.

Dumas, H.S., Ellison, J.A. & Sáenz, A.W. (1991).  Axial channeling in perfect crystals, the continuum model, and the method of averaging.  Annals of Physics (NY) 209: 97–123.

Dumas, H.S.  (1991).  Ergodization rates for linear flow on the torus.  Journal of Dynamics and Differential Equations 3 (4): 593–610.

Dumas, H.S. & Kimball, J. (1990).  Symmetry in motion, relation to chaos.  Physics Letters A 144:  201–205.

Ellison, J.A., Sáenz, A.W. & Dumas, H.S. (1990).  Improved Nth order averaging for periodic systems.  Journal of Differential Equations 84: 383–403.

Dumas, H.S.  (1989).  Nekhoroshev's theorem and particle channeling in crystals, in Integrable Systems and Applications (M. Balabane, P. Lochak, and C. Sulem, Eds.) Lecture Notes in Physics No. 342: 87–94, Springer-Verlag, New York.

Dumas, H.S. & Ellison, J.A.  (1986).  Particle channeling and the method of averaging, in Local and Global Methods of Nonlinear Dynamics (R. Cawley, A.W. Sáenz, and W.W. Zachary, Eds.) Lecture Notes in Physics No. 252: 200–230, Springer-Verlag, New York.

Other Publication

Dumas, H.S. (2014).  KAM Theory (book blurb), in The Right Angle (Newsletter of the University of Cincinnati Department of Mathematical Sciences) Vol. 21, Fall 2014, page 2.

Palacián, J.F., Yanguas, P. & Dumas, H.S. (2013).  Preface to Special Issue on Hamiltonian Systems and Celestial Mechanics, Qualitative Theory of Dynamical Systems  12 (1) : 1–3 (DOI  10.1007/s12346-013-0100-x).

Dumas, H.S. & Golse, F.  (2013).  The Lorentz gas: periodic or not? Notes of the Canadian Mathematical Society (research notes section) 45 (1) 16–17.

Dumas, H.S. (2011).  Hamiltonian dynamics and celestial mechanics, a conference in honor of Ken Meyer in his 75th year.  Dynamical Systems Magazine (July, 2011, section: Dynamical Systems Today, 3 pp., electronic)

Dumas, H.S. (2011).  A brief biographical sketch of Ken Meyer. Dynamical Systems Magazine (July, 2011, section: In the Spotlight, 5 pp., electronic)

Dumas, H.S. (2008).  Oscillations near the eye of the long-tailed fish, Electronic Journal of Differential Equations, Differential Equations Problems Page, Problem 2007–1; Solution 2008.

Dumas, H.S. (2004).  More than 30 signed reviews of articles in Mathematical Reviews/MathSciNet, 1999–2004.

Dumas, H.S. (1996).  Review of the book Classical Dynamics with Applications to Beam Dynamics, by L. Michelotti, Wiley Interscience, New York, 1994, in SIAM Review 38 (4): 685–687.

Dumas, H.S.  (1992).  The role of low-dimensional symplectic maps in the dynamics of particle accelerators.  Imagine That!  (The Geometry Center Quarterly, University of Minnesota) 1 (2): 6–7.

Lecture

(01-09-2020. ) Mathematics Colloquium .Institute of Mathematics, Academia Sinica, Taipei, Taiwan.

(01-07-2020. ) Applied Mathematics Seminar .Institute of Mathematics, Academia Sinica, Taipei, Taiwan.

(01-02-2020. ) Applied Mathematics Seminar .National Sun Yat-sen University, Kaohsiung, Taiwan.

(12-10-2019. ) Applied Mathematics Seminar .University of New Mexico, Albuquerque, NM.

(11-15-2017. ) Keynote speaker .Opening Ceremony of 7th Sino-Foreign Postgraduate Academic Forum, Jiangsu University, Zhenjiang, China.

(03-16-2015. ) Applied Mathematics Seminar .University of New Mexico, Albuquerque, NM.

(04-16-2010. ) Seminar in KAM theory 2 .Jiangsu University, Zhenjiang, China.

(04-15-2010. ) Seminar in KAM theory 1 .Jiangsu University, Zhenjiang, China.

(06-07-2006. ) Invited talk .International Conference on Nonlinear and Stochastic Dynamics, Chengdu, China.

(02-23-2006. ) Seminar in Harmonic Analysis and PDE .University of New Mexico, Albuquerque, NM.

(10-11-2005. ) Joint DESY/University of Hamburg Physics Seminar, DESY-MPY .Hamburg, Germany.

(09-15-2005. ) Theoretical Physics Seminar .University of Warwick, Coventry, England.

(02-2005. ) Invited lectures, Matemairacorana .Universidade Federal de Pernambuco, Recife, Brazil.

(03-24-2004. ) Invited talk .Workshop on Relativistic Channeling, Frascati, Italy.

(07-29-2003. ) Oberseminar, IRAM .Rheinisch-Westfaelische Technische Hochschule, Aachen, Germany.

(07-22-2003. ) Invited talk, Equadiff 2003 .Limburg University, Hasselt, Belgium.

(04-25-2002. ) Mathematics Colloquium .University of Cincinnati, OH.

(03-19-2002. ) Seminar in Perturbation Theory .University of New Mexico, Albuquerque, NM.

(01-17-2002. ) Physics Colloquium .University of Cincinnati, OH.

(09-14-2001. ) Applied Mathematics Seminar .University of New Mexico, Albuquerque, NM.

(04-16-2001. ) PACM Dynamical Systems/Nonlinear Science Seminar .Princeton University, NJ.

(05-18-2000. ) Audition, Laboratoire de mathématiques .Université d’Orléans, France.

(03-22-2000. ) Séminaire systèmes dynamiques .Université de Lille I, France.

(10-17-1988. ) Lefschetz Center for Dynamics Colloquium .Brown University, Providence, RI.

(10-11-1988. ) Physics Colloquium .SUNY-Albany, NY.

(06-23-1988. ) Invited Talk, Conference on Integrable Systems & Applications .Ile d'Oléron, France.

(04-27-1988. ) Mathematics Colloquium .San Jose State University, CA.

(07-08-1987. ) Condensed Matter Theory Seminar .Naval Research Laboratory, Washington, DC.

(07-08-1987. ) Condensed Matter Theory Seminar .Naval Research Laboratory, Washington, DC.

(12-19-1986. ) Séminaire phénomènes non-linéaires .Ecole Polytechnique, Palaiseau, France.

(12-12-1986. ) Séminaire Centre de Maths Appliquées .ENS-Paris, France.

(11-24-1986. ) Séminaire Institut de Physique Nucléaire .Université de Lyon I, Lyon, France.

(06-26-1985. ) Condensed Matter Theory Seminar .Naval Research Laboratory, Washington, DC.

Event Organized

05-2011 Hamiltonian Dynamics and Celestial Mechanics, a Conference in Honor of Ken Meyer in his 75th year, Castro Urdiales, Spain

12-2006 Workshop on Theory & Applications of Fluid Mechanics, University of Cincinnati

09-2002 Midwest Dynamical Systems Seminar, University of Cincinnati

09-2000 30th Anniversary Midwest Dynamical Systems Conference, University of Cincinnati

05-1995 Minisymposium, 3rd SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah

03-1992 International Conference on Hamiltonian Dynamical Systems, University of Cincinnati

2009 Representative of Excellence in Teaching, Greater Cincinnati Consortium of Colleges & Universities

2009 Edith C. Alexander Award for Distinguished Teaching, College of Arts and Sciences, University of Cincinnati

2008 Mrs. A.B. (Dolly) Cohen Award for Outstanding Contributions and Excellence in Teaching, University of Cincinnati

1994 Qualification aux fonctions de professeur des universités, French Ministry of Higher Education and Research

1991 Tom L. Popejoy Dissertation Prize (Best PhD Thesis in the Sciences, Mathematics, or Engineering during the period 1987–90), University of New Mexico