Applied Mathematics

People Research Teaching Publications

  • Books:
    1. M. Kunze: Non-Smooth Dynamical Systems,
           Lecture Notes in Mathematics Vol. 1744, Springer
           Berlin-New York 2000

    2. M. Kunze: A Birman-Schwinger Principle in Galactic Dynamics,
           Birkhäuser/Springer, Cham 2021

  • Papers:

  • IMPORTANT NOTE: The files to download are preprints but not the final versions that did appear or that are to appear.
    1. M. Kunze: On the uniqueness and asymptotic behaviour
           of plasma corners,
           Z. Anal. Anwendungen 13, 629-644 (1994)

    2. M. Kunze: On a special class of nonlinear integral equations,
           J. Integral Equations Appl. 7, 329-350 (1995)

    3. M. Kunze: On zeros of semicondensing operators,
           Nonlinear Anal. 26, 313-321 (1996)

    4. M. Kunze & M.D.P. Monteiro Marques: B.V. solutions
           to evolution problems with time-dependent domains,
           C. R. Acad. Sci. Paris Sér. I Math. 323, 993-998 (1996)

    5. M. Kunze: A nonlinear characterization of Hilbert spaces,
           J. Math. Anal. Appl. 204, 627-630 (1996)

    6. M. Kunze & M.D.P. Monteiro Marques: Yosida-Moreau regularization
           of sweeping processes with unbounded variation,
           J. Differential Equations 130, 292-306 (1996)

    7. M. Kunze: A note on a paper of Cellina concerning
           differential equations in Banach spaces,
           Bull. London Math. Soc. 28, 613-616 (1996)

    8. M. Kunze & T. Küpper: Qualitative bifurcation analysis
           of a non-smooth friction-oscillator model,
           Z. Angew. Math. Phys. 48, 87-101 (1997)

    9. A. Komech, H. Spohn & M. Kunze: Long-time asymptotics for
           a classical particle interacting with a scalar wave field,
           Comm. Partial Differential Equations 22, 307-335 (1997)

    10. M. Kunze & M.D.P. Monteiro Marques: Existence of solutions
            for degenerate sweeping processes,
            J. Convex Anal. 4, 165-176 (1997)

    11. M. Kunze & M.D.P. Monteiro Marques: BV solutions
            to evolution problems with time-dependent domains,
            Set-Valued Anal. 5, 57-72 (1997)

    12. M. Kunze & J. Neumann: Linear complementary problems
            and the simulation of the motion of rigid body systems,
            Z. Ang. Math. Mech. 77, 833-838 (1997)

    13. M. Kunze, T. Küpper & J. You: On the application of KAM theory
            to discontinuous dynamical systems,
            J. Differential Equations 139, 1-21 (1997)

    14. M. Kunze & G. Schlüchtermann: Strongly generated Banach spaces
            and measures of non-compactness,
            Math. Nachrichten 191, 197-214 (1998)

    15. M. Kunze & M.D.P. Monteiro Marques: Discretization methods
            for degenerate sweeping processes,
            Portugaliae Mathematica 55, 219-232 (1998)

    16. J. Batt, M. Kunze & G. Rein: On the asymptotic behaviour
            of a one-dimensional, monocharged plasma and a rescaling method,
            Advances in Differential Equations 3, 271-292 (1998)

    17. M. Kunze: Instability of the periodic motion of a particle interacting
            with a scalar wave field,
            Comm. Math. Phys. 195, 509-523 (1998)

    18. M. Kunze: Unbounded solutions in non-smooth dynamical systems
            at resonance,
            Z. Ang. Math. Mech. 78, Supplement 3, S985-S986 (1998)

    19. M. Kunze & M.D.P. Monteiro Marques: On parabolic quasi-variational
            inequalities and state-dependent sweeping processes,
            Topological Methods in Nonlinear Analysis 12, 179-191 (1998)

    20. M. Kunze & M.D.P. Monteiro Marques: Degenerate sweeping processes,
            in: Proc. IUTAM Symposium on Variations of Domains
            and Free-Boundary Problems in Solid Mechanics, Paris 1997,
            Eds. P. Argoul, M. Frémond & Q.S. Nguyen, Kluwer Acad. Press,
            Dordrecht 1999, pp. 301-307

    21. M. Kunze: Periodic solutions of nonlinear kinematic hardening models,
            Math. Meth. Appl. Sci. 22, 515-529 (1999)

    22. M. Kunze, T. Küpper, V.K. Mezentsev, E.G. Shapiro & S. Turitsyn:
            Nonlinear solitary waves with Gaussian tails,
            Physica D 128, 273-295 (1999)

    23. M. Kunze: Periodic solutions of conservative non-smooth
            dynamical systems,
            Z. Ang. Math. Mech. 79, Supplement 1, S97-S100 (1999)

    24. A. Komech, M. Kunze & H. Spohn: Effective dynamics
            for a mechanical particle coupled to a wave field,
            Comm. Math. Phys. 203, 1-19 (1999)

    25. M. Kunze & M.D.P. Monteiro Marques: A note on Lipschitz continuous
            solutions of a parabolic quasi-variational inequality,
            in: Luso-Chinese Symposium on Nonlinear Evolution Equations,
            Macau 1998, Eds. Ta-tsien Li, Long-wei Lin & J.F. Rodrigues
            World Scientific, Singapore-New Jersey-London 1999, pp. 109-115

    26. M. Kunze, T. Küpper & Y. Li: On Conley index theory
            for non-smooth dynamical systems,
            Differential Integral Equations 13, 479-502 (2000)

    27. M. Kunze: On Lyapunov exponents for non-smooth dynamical systems
            with an application to a pendulum with dry friction,
            J. Dynamics Differential Equations 12, 31-116 (2000)

    28. M. Kunze: Rigorous methods and numerical results
            for dry friction problems,
            Chapter 9 of the book: M. Wiercigroch & B. de Kraker:
            Applied Nonlinear Dynamics and Chaos of Mechanical Systems with
            Discontinuities, World Scientific, Singapore-New Jersey-London 2000

    29. M. Kunze & J.F. Rodrigues: An elliptic quasi-variational inequality
            with gradient constraint and some of its applications,
            Math. Meth. Appl. Sci. 23, 897-908 (2000)

    30. M. Kunze & H. Spohn: Radiation reaction and center manifolds,
            SIAM J. Math. Anal. 32, 30-53 (2000)

    31. M. Kunze & H. Spohn: Slow motion of charges interacting through
            the Maxwell field,
            Comm. Math. Phys. 212, 437-467 (2000)

    32. M. Kunze & M.D.P. Monteiro Marques: An introduction
            to Moreau's sweeping process,
            in: Impacts in Mechanical Systems - Analysis and Modelling,
            Ed. B. Brogliato, Lecture Notes in Physics Vol. 551, Springer,
            Berlin-New York 2000, pp. 1-60

    33. M. Kunze: Effective dynamics for the Maxwell-Lorentz system,
            in: International Conference on Differential Equations (Equadiff 99),
            Berlin 1999, Eds. B. Fiedler, K. Gröger & J. Sprekels, Vol. 1,
            World Scientific, Singapore-New Jersey-London 1999, pp. 109-111

    34. M. Kunze & H. Spohn: Adiabatic limit for the
            Abraham-Lorentz equations,
            Ann. H. Poincaré 1, 625-653 (2000)

    35. M. Kunze: Remarks on boundedness of semilinear oscillators,
            in: Nonlinear Analysis and its Applications to Differential Equations,
            Lisbon 1998, Eds. M.R. Grossinho, M. Ramos, C. Rebelo & L. Sanchez,
            Progress in Nonlinear Differential Equations and Their Applications
            Vol. 43, Birkhäuser, Basel-Boston 2001, pp. 311-320

    36. M. Kunze & T. Küpper: Nonsmooth dynamical systems: An overview,
            in: Ergodic Theory, Analysis, and Efficient Simulation
            of Dynamical Systems, Ed. B. Fiedler, Springer, Berlin-New York 2001,
            pp. 431-452

    37. M. Kunze, T. Küpper & B. Liu: Boundedness and unboundedness
            of solutions for reversible oscillators at resonance,
            Nonlinearity 14, 1105-1122 (2001)

    38. M. Kunze: Bifurcation from the continuous spectrum
            without sign condition on the nonlinearity,
            Proc. Roy. Soc. Edinburgh, Ser. A 131, 927-943 (2001)

    39. M. Kunze: Periodic solutions of a singular Lagrangian system
            related to dispersion-managed fiber communication devices,
            Nonlinear Dynamics and Systems Theory 1, 159-167 (2001)

    40. M. Kunze & A.D. Rendall: The Vlasov-Poisson system
            with radiation damping,
            Ann. H. Poincaré 2, 857-886 (2001)

    41. M. Kunze: On the period of periodic motions of a particle
            in a scalar wave field,
            Z. Ang. Math. Mech. 81, Supplement 3, S603-S606 (2001)

    42. M. Kunze & A.D. Rendall: Simplified models of electromagnetic
            and gravitational radiation damping,
            Classical Quantum Gravity 18, 3573-3587 (2001)

    43. M. Kunze & H. Spohn: Post-Coulombian dynamics at order c^{-3},
            J. Nonlinear Science 11, 321-396 (2001)

    44. M. Kunze & H. Spohn: Slow motion of charges interacting
            through the Maxwell field,
            in: XIIIth International Congress on Mathematical Physics,
            London 2000, Eds. A. Grigoryan, A. Fokas, T. Kibble & B. Zegarlinski,
            International Press, Boston 2001, pp. 219-224

    45. M. Kunze & B. Michaeli: On the rigorous applicability
            of Oseledets' theorem to obtain Lyapunov exponents
            for non-smooth dynamical systems,
            to appear (!?) in Proc. 2. Int. Conf. Diff. Equ., Marrakesh 1995,
            Ed. O. Arino

    46. M. Kunze: The singular perturbation limit of a variational problem
            from nonlinear fiber optics,
            Phys. D 180, 108-114 (2003)

    47. M. Kunze: On the existence of a maximizer for the Strichartz inequality,
            Comm. Math. Phys. 243, 137-162 (2003)

    48. M. Kunze: On a variational problem with lack of compactness related
            to the Strichartz inequality,
            Calc. Var. Partial Differential Equations 19, 307-336 (2004)

    49. Th. Brand, M. Kunze, G. Schneider & Th. Seelbach: Hopf bifurcation
            and exchange of stability in diffusive media,
            Arch. Rat. Mech. Anal. 171, 263-296 (2004)

    50. M. Kunze & G. Schneider: Exchange of stability
            and finite-dimensional dynamics in a bifurcation problem
            with marginally stable continuous spectrum,
            Z. Angew. Math. Phys. 55, 383-399 (2004)

    51. M. Kunze & R. Ortega: On the number of solutions
            to semilinear boundary value problems,
            Adv. Nonlinear Stud. 4, 237-249 (2004)

    52. M. Kunze, J. Moeser & V. Zharnitsky: Ground states
            for the higher order dispersion managed NLS equation
            in the absence of average dispersion,
            J. Differential Equations 209, 77-100 (2005)

    53. S. Bauer & M. Kunze: The Darwin approximation
            of the relativistic Vlasov-Maxwell system,
            Ann. H. Poincaré 6, 283-308 (2005)

    54. M. Kunze & G. Schneider: Estimates for the KdV-limit
            of the Camassa-Holm equation,
            Lett. Math. Phys. 72, 17-26 (2005)

    55. A. Komech, E. Kopylova & M. Kunze: Dispersive estimates
            for 1D discrete Schrödinger and Klein-Gordon equations,
            Appl. Anal. 85, 1487-1508 (2006)

    56. S. Bauer, M. Kunze, G. Rein & A.D. Rendall: Multipole radiation
            in a collisionless gas coupled to electromagnetism or scalar gravitation,
            Comm. Math. Phys. 266, 267-288 (2006)

    57. S. Bauer & M. Kunze: Radiative friction for charges interacting with the
            Maxwell field: Classical many-particle systems,
            in: Analysis, Modeling and Simulation of Multiscale Problems,
            Ed. A. Mielke, Springer, Berlin-New York 2006, pp. 531-551

    58. M. Kunze: Mathematical results related to dispersion management
            in nonlinear optical fibers,
            Oberwolfach Reports 4, 2628-2630 (2007)

    59. M. Kunze & R. Ortega: Complete orbits for twist maps on the plane,
            Ergodic Theory Dynam. Systems 28, 1197-1213 (2008)

    60. M. Kunze: Multipole radiation in classical particle systems,
            Oberwolfach Reports 5, 389-392 (2008)

    61. H. Andréasson, M. Kunze & G. Rein: Global existence
            for the spherically symmetric Einstein-Vlasov system
            with outgoing matter,
            Comm. Partial Differential Equations 33, 656-668 (2008)

    62. H. Andréasson, M. Kunze & G. Rein: Gravitational collapse
            and the formation of black holes for the spherically symmetric
            Einstein-Vlasov system,
            Quarterly Applied. Math. 68, 17-42 (2010) [W. Strauss anniversary volume]

    63. M. Kunze: On the absence of radiationless motion for a rotating classical charge,
            Adv. Math. 223, 1632-1665 (2010)

    64. H. Andréasson, M. Kunze & G. Rein: The formation of black holes
            in spherically symmetric gravitational collapse,
            Math. Ann. 350, 683-705 (2011)

    65. M. Kunze & R. Ortega: Complete orbits for twist maps on the plane:
            extensions and applications,
            J. Dynamics Differential Equations 23, 405-423 (2011) [R. Johnson anniversary volume]

    66. M. Kunze & R. Ortega: Complete orbits for twist maps on the plane:
            the case of small twist,
            Ergodic Theory Dynam. Systems 31, 1471-1498 (2011)

    67. H. Andréasson, M. Kunze & G. Rein: Existence of axially symmetric static solutions
            of the Einstein-Vlasov system,
            Comm. Math. Phys. 308, 23-47 (2011)

    68. M. Kunze & R. Ortega: Twist mappings with non-periodic angles,
            in: Stability and Bifurcation Theory for Non-Autonomous Differential Equations,
            Lecture Notes in Mathematics Vol. 2065,
            Eds. R. Johnson & M.P. Pera, Springer, Berlin-New York 2013, pp. 265-300

    69. M. Kunze & R. Ortega: Long-time stability estimates
            for the non-periodic Littlewood boundedness problem,
            Proc. London Math. Soc. 107, 39-75 (2013)

    70. H. Andréasson, M. Kunze & G. Rein: Rotating, stationary, axially symmetric
            spacetimes with collisionless matter,
            Comm. Math. Phys. 329, 787-808 (2014)

    71. M. Kunze & D.M.A. Stuart: Nekhoroshev type stability results for Hamiltonian systems
            with an additional transversal component,
            J. Math. Anal. Appl. 419, 1351-1386 (2014)

    72. H.M. Huynh & M. Kunze: Partner orbits and action differences on compact factors
            of the hyperbolic plane. Part I: Sieber-Richter pairs,
            Nonlinearity 28, 593-623 (2015)

    73. M. Kunze: Yet another criterion for global existence
            in the 3D relativistic Vlasov-Maxwell system,
            J. Differential Equations 259, 4413-4442 (2015)

    74. M. Kunze & R. Ortega: Almost surely recurrent motions in the Euclidean space,
            Proc. Amer. Math. Soc. 145, 4345-4351 (2017)

    75. M. Kunze: Higher regularity of the 'tangential' fields
            in the relativistic Vlasov-Maxwell system,
            J. Differential Equations 265, 2778-2792 (2018)

    76. H. Andréasson & M. Kunze: Comments on the paper 'Static solutions
            of the Vlasov-Einstein system' by G. Wolansky,
            Arch. Rat. Mech. Anal. 235, 783-791 (2019)

    77. M. Kunze & R. Ortega: Escaping orbits are rare
            in the quasi-periodic Fermi-Ulam ping-pong,
            Ergodic Theory Dynam. Systems 40, 975-991 (2020)

    78. M. Kunze & R. Ortega: Growth rates of orbits in non-periodic twist maps
            and a theorem by Neishtadt,
            Nonlinearity 34, 3732-3761 (2021)

    79. M. Kunze & R. Ortega: Hamiltonian normal forms and applications to maps,
            also available from

    80. M. Kunze: A second look at the Kurth solution
            in galactic dynamics, R. Glassey memorial issue,
            Kinet. Relat. Models 15, 651-662 (2022)

    81. M. Kunze: A Birman-Schwinger principle in galactic dynamics:
            ESI, Vienna, 07-11 February 2022,
            Classical Quantum Gravity 39, 244001 (2022)

    82. H. Andréasson & M. Kunze: Static solutions to the spherically symmetric Einstein-Vlasov system:
            a particle-number-Casimir approach,
            to appear in SIAM J. Math. Anal.

    83. É. Amorim, H. Andréasson & M. Kunze: Proof of the Einstein quadrupole formula for solutions of the
            Einstein-Vlasov system close to Minkowski spacetime,
            also available from

  • Theses:

    1. Das relativistische Vlasov-Maxwell-System partieller Differential-
           gleichungen zu Anfangsdaten mit nichtkompaktem Träger,
           Diploma thesis, Ludwig Maximilians-Universität München 1991 (238 pp.)

    2. Beiträge zur Theorie halbverdichtender Operatoren in Banachräumen
           mit einer Anwendung auf ein freies Randwertproblem aus der
           Ph.D. thesis, Ludwig Maximilians-Universität München 1994 (133 pp.)

    3. Contributions to the Theory of Semicondensing Vectorfields
           in Banach spaces with an Application to a Free Boundary Problem
           Arising in Plasma Physics
           (english translation of 2.)

    4. Non-Smooth Dynamical Systems
           Habilitation thesis, Universität zu Köln 1998 (153 pp.)

    Last updated: September 04, 2023