Publications



    Monograph

    Jointly with Nora Doll and Hermann Schulz-Baldes I have written a book on various topics about the spectral flow. It can be downloaded here:

    Spectral Flow - A Functional Analytic and Index-Theoretic Approach

    De Gruyter Studies in Mathematics 94

    Preprints

  1. J. Janczewska, M. Möckel, N. Waterstraat
    Bifurcation for a Class of Indefinite Elliptic Systems by Comparison Theory for the Spectral Flow via an Index Theorem
    \arxiv:2405.19473

  2. J. Janczewska, M. Izydorek, M. Starostka, N. Waterstraat
    The Equivariant Spectral Flow and Bifurcation for Functionals with Symmetries -- Part I
    \arXiv:2306.01170

  3. J. Janczewska, M. Izydorek, N. Waterstraat
    Periodic solutions of Lagrangian systems under small perturbations
    acepted for publication in Communications in Contemporary Mathematics

  4. M. Starostka, N. Waterstraat
    Lecture notes on the relative cup-length for the Conley index and the Arnold conjecture

  5. T. O. Rot, M. Starostka, N. Waterstraat
    The relative cup-length in local Morse cohomology
    \arXiv:2212.10309, accepted for publication in TMNA


    6. Published Papers

  6. R. Skiba, N. Waterstraat
    The Index Bundle for Selfadjoint Fredholm Operators and Multiparameter Bifurcation for Hamiltonian Systems
    Z. Anal. Anwend. 41, 2023, 487-501

  7. R. Skiba, N. Waterstraat
    Fredholm theory of families of discrete dynamical systems and its applications to bifurcation theory
    Discrete Contin. Dyn. Syst. 43, 2023, 1878-1904

  8. M. Starostka, N. Waterstraat
    On a Comparison Principle and the Uniqueness of Spectral Flow
    Math. Nachr. 295, 2022, 785--805

  9. M. Izydorek, J. Janczewska, N. Waterstraat
    The Equivariant Spectral Flow and Bifurcation of Periodic Solutions of Hamiltonian Systems
    Nonlinear Anal. 211, 2021

  10. M. Izydorek, J. Janczewska, N. Waterstraat
    Homoclinics for Singular Strong Force Lagrangian Systems in R^N
    Calc. Var. Partial Differential Equations 60, 2021

  11. N. Waterstraat
    On the Fredholm Lagrangian Grassmannian, Spectral Flow and ODEs in Hilbert Spaces
    J. Differential Equations 303, 2021, 667-700

  12. J. Ciesielski, J. Janczewska, N. Waterstraat
    On the existence of homoclinic type solutions for a class of inhomogenous second order Hamiltonian systems
    J. Dynam. Differential Equations 32, 2020, 1343-1356

  13. N. Doll, H. Schulz-Baldes, N. Waterstraat
    Parity as $\mathbb{Z}_2$-valued Spectral Flow
    Bull. London Math. Soc. 51, 2019, 836--852

  14. M. Izydorek, J. Janczewska, N. Waterstraat,
    The Maslov Index and the Spectral Flow-revisited
    Fixed Point Theory and Applications, 2019, Article Nr. 5

  15. M. Starostka, N. Waterstraat,
    The E-cohomological Conley Index, Cup-lengths and the Arnold Conjecture on T^{2n}
    Advanced Nonlinear Studies 19, 2019, 519-528

  16. G. Marchesi, A. Portaluri, N. Waterstraat,
    Not every conjugate point of a semi-Riemannian geodesic is a bifurcation point
    Differential Integral Equations 31, 2018, 871-880

  17. M. Izydorek, J. Janczewska, N. Waterstraat, A. Zgorzelska,
    Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation
    Nonlinear Anal. Real World Appl. 39, 2018, 451-463

  18. N. Waterstraat,
    A Remark on Bifurcation of Fredholm Maps
    Adv. Nonlinear Anal. 7, 2018, 285-292

  19. A. Portaluri, N. Waterstraat,
    Corrigendum to "A Morse-Smale index theorem for indefinite elliptic systems and bifurcation'' [J. Differential Equations 258 (5) (2015) 1715-1748]
    J. Differential Equations 264, 2018, 3067-3069

  20. N. Waterstraat,
    Spectral flow and bifurcation for a class of strongly indefinite elliptic systems
    Proc. Royal Soc. Edinburgh A 148, 2018, 1097-1113

  21. R. Skiba, N. Waterstraat,
    The Index Bundle and Multiparameter Bifurcation for Discrete Dynamical Systems
    Discrete Contin. Dynam. Systems 37, 2017, 5603-5629

  22. A. Portaluri, N. Waterstraat,
    A K-theoretical Invariant and Bifurcation for Homoclinics of Hamiltonian Systems
    J. Fixed Point Theory Appl. 19, 2017, 833-851

  23. J. Ciesielski, J. Janczewska, N. Waterstraat,
    On the existence of homoclinic type solutions of inhomogenous Lagrangian systems
    Differential Integral Equations 30, 2017, 259-272

  24. N. Waterstraat,
    Fredholm Operators and Spectral Flow
    Rend. Sem. Mat. Univ. Politec. Torino 75, 2017, 7-51

  25. A.M. Candela, N. Waterstraat,
    Bifurcation of critical points along gap-continuous families of subspaces
    J. Fixed Point Theory Appl. 19, 2017, 3053-3068

  26. F. Bei, N. Waterstraat,
    On the space of connections having non-trivial twisted harmonic spinors
    J. Math. Phys. 56, 2015

  27. N. Waterstraat,
    Spectral flow, crossing forms and homoclinics of Hamiltonian systems
    Proc. Lond. Math. Soc. (3) 111, 2015, 275-304

  28. N. Waterstraat,
    On bifurcation for semilinear elliptic Dirichlet problems on shrinking domains
    Springer Proc. Math. Stat. 119, 2015, 273-291

  29. A. Portaluri, N. Waterstraat,
    Yet another proof of the Morse index theorem
    Expositiones Math. 33, 2015, 378-386

  30. N. Waterstraat,
    A family index theorem for periodic Hamiltonian systems and bifurcation
    Calculus of Variations and PDE 52, 2015, 727-753

  31. M. Starostka, N. Waterstraat,
    A remark on singular sets of vector bundle morphisms
    European J. Math. 1, 154-159

  32. A. Portaluri, N. Waterstraat,
    A Morse-Smale index theorem for indefinite elliptic systems and bifurcation
    J. Differential Equations 258, 2015, 1715-1748

  33. A. Portaluri, N. Waterstraat,
    On bifurcation for semilinear elliptic Dirichlet problems on geodesic balls
    J. Math. Anal. Appl. 415, 2014, 240-246

  34. A. Portaluri, N. Waterstraat,
    Bifurcation results for critical points of families of functionals
    Differential Integral Equations 27, 2014, 369-386

  35. J. Pejsachowicz, N. Waterstraat,
    Bifurcation of critical points for continuous families of $C^2$ functionals of Fredholm type
    J. Fixed Point Theory Appl. 13, 2013, 537-560

  36. A. Portaluri, N. Waterstraat,
    On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem
    J. Math. Anal. Appl. 408, 2013, 572-575

  37. N. Waterstraat,
    A remark on the space of metrics having non-trivial harmonic spinors
    J. Fixed Point Theory Appl. 13, 2013, 143-149

  38. N. Waterstraat,
    A K-theoretic proof of the Morse index theorem in semi-Riemannian geometry
    Proc. Amer. Math. Soc. 140, 2012, 337-349

  39. N. Waterstraat,
    The index bundle for Fredholm morphisms
    Rend. Sem. Mat. Univ. Politec. Torino 69, 2011, 299-315


    40. Other Publications

  40. C. Luleich, N. Waterstraat, P. Reiter,
    Modelling Mathematical Knowledge from Natural Language Representations. Introducing a New Method
    Paper presented at the AECT, Jacksonville, FL, 2020

  41. N. Waterstraat,
    1,2,3...'ne Menge! Wie viel ist Unendlich?
    Cantor-Heft 21 der Georg-Cantor-Vereinigung, 2019, 9-18

  42. N. Waterstraat,
    The index bundle for gap-continuous families and the spectral flow
    Oberwolfach Rep. 9, 2012, 1530-1532