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
- 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
- J. Janczewska, M. Izydorek, M. Starostka, N. Waterstraat
The Equivariant Spectral Flow and Bifurcation for Functionals with Symmetries -- Part I
\arXiv:2306.01170
- J. Janczewska, M. Izydorek, N. Waterstraat
Periodic solutions of Lagrangian systems under small perturbations
acepted for publication in Communications in Contemporary Mathematics
- M. Starostka, N. Waterstraat
Lecture notes on the relative cup-length for the Conley index and the Arnold conjecture
- T. O. Rot, M. Starostka, N. Waterstraat
The relative cup-length in local Morse cohomology
\arXiv:2212.10309, accepted for publication in TMNA
Published Papers
- R. Skiba, N. Waterstraat
The Index Bundle for Selfadjoint Fredholm Operators and Multiparameter Bifurcation for Hamiltonian Systems
Z. Anal. Anwend. 41, 2023, 487-501
- 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
- M. Starostka, N. Waterstraat
On a Comparison Principle and the Uniqueness of Spectral Flow
Math. Nachr. 295, 2022, 785--805
- M. Izydorek, J. Janczewska, N. Waterstraat
The Equivariant Spectral Flow and Bifurcation of Periodic Solutions of Hamiltonian Systems
Nonlinear Anal. 211, 2021
- M. Izydorek, J. Janczewska, N. Waterstraat
Homoclinics for Singular Strong Force Lagrangian Systems in R^N
Calc. Var. Partial Differential Equations 60, 2021
- N. Waterstraat
On the Fredholm Lagrangian Grassmannian, Spectral Flow and ODEs in Hilbert Spaces
J. Differential Equations 303, 2021, 667-700
- 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
- N. Doll, H. Schulz-Baldes, N. Waterstraat
Parity as $\mathbb{Z}_2$-valued Spectral Flow
Bull. London Math. Soc. 51, 2019, 836--852
- M. Izydorek, J. Janczewska, N. Waterstraat,
The Maslov Index and the Spectral Flow-revisited
Fixed Point Theory and Applications, 2019, Article Nr. 5
- 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
- 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
- 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
- N. Waterstraat,
A Remark on Bifurcation of Fredholm Maps
Adv. Nonlinear Anal. 7, 2018, 285-292
- 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
- N. Waterstraat,
Spectral flow and bifurcation for a class of strongly indefinite elliptic systems
Proc. Royal Soc. Edinburgh A 148, 2018, 1097-1113
- R. Skiba, N. Waterstraat,
The Index Bundle and Multiparameter Bifurcation for Discrete Dynamical Systems
Discrete Contin. Dynam. Systems 37, 2017, 5603-5629
- A. Portaluri, N. Waterstraat,
A K-theoretical Invariant and Bifurcation for Homoclinics of Hamiltonian Systems
J. Fixed Point Theory Appl. 19, 2017, 833-851
- J. Ciesielski, J. Janczewska, N. Waterstraat,
On the existence of homoclinic type solutions of inhomogenous Lagrangian systems
Differential Integral Equations 30, 2017, 259-272
- N. Waterstraat,
Fredholm Operators and Spectral Flow
Rend. Sem. Mat. Univ. Politec. Torino 75, 2017, 7-51
- A.M. Candela, N. Waterstraat,
Bifurcation of critical points along gap-continuous families of subspaces
J. Fixed Point Theory Appl. 19, 2017, 3053-3068
- F. Bei, N. Waterstraat,
On the space of connections having non-trivial twisted harmonic spinors
J. Math. Phys. 56, 2015
- N. Waterstraat,
Spectral flow, crossing forms and homoclinics of Hamiltonian systems
Proc. Lond. Math. Soc. (3) 111, 2015, 275-304
- N. Waterstraat,
On bifurcation for semilinear elliptic Dirichlet problems on shrinking domains
Springer Proc. Math. Stat. 119, 2015, 273-291
- A. Portaluri, N. Waterstraat,
Yet another proof of the Morse index theorem
Expositiones Math. 33, 2015, 378-386
- N. Waterstraat,
A family index theorem for periodic Hamiltonian systems and bifurcation
Calculus of Variations and PDE 52, 2015, 727-753
- M. Starostka, N. Waterstraat,
A remark on singular sets of vector bundle morphisms
European J. Math. 1, 154-159
- A. Portaluri, N. Waterstraat,
A Morse-Smale index theorem for indefinite elliptic systems and bifurcation
J. Differential Equations 258, 2015, 1715-1748
- A. Portaluri, N. Waterstraat,
On bifurcation for semilinear elliptic Dirichlet problems on geodesic balls
J. Math. Anal. Appl. 415, 2014, 240-246
- A. Portaluri, N. Waterstraat,
Bifurcation results for critical points of families of functionals
Differential Integral Equations 27, 2014, 369-386
- 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
- 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
- N. Waterstraat,
A remark on the space of metrics having non-trivial harmonic spinors
J. Fixed Point Theory Appl. 13, 2013, 143-149
- N. Waterstraat,
A K-theoretic proof of the Morse index theorem in semi-Riemannian geometry
Proc. Amer. Math. Soc. 140, 2012, 337-349
- N. Waterstraat,
The index bundle for Fredholm morphisms
Rend. Sem. Mat. Univ. Politec. Torino 69, 2011, 299-315
Other Publications
- 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
- N. Waterstraat,
1,2,3...'ne Menge! Wie viel ist Unendlich?
Cantor-Heft 21 der Georg-Cantor-Vereinigung, 2019, 9-18
- N. Waterstraat,
The index bundle for gap-continuous families and the spectral flow
Oberwolfach Rep. 9, 2012, 1530-1532