Prof. Dr. Hans-Otto Walther — Publications
Monographs
[2] with T. Krisztin and J. Wu: Shape, smoothness, and invariant stratification of an attracting set for delayed monotone positive feedback.
Fields Institute Monograph series vol. 11, A.M.S., Providence 1999.
[1]

with O. Diekmann, S.A. van Gils, and S.M. Verduyn Lunel: Delay Equations: Functional-, Complex- and Nonlinear Analysis.
Springer, New York 1995.
Preprints
[5] Algebraic-delay differential systems, state-dependent delay, and temporal order of reactions.
41 pp, 2008.
[4] with R. Qesmi: Center-stable manifolds for differential equations with state-
dependent delay.
31 pp, 2007, to appear in Discrete and Continuous Dynamical Systems.
[3] with P. Brunovský and A. Erdélyi: Short-term fluctuations of exchange rates driven by expectations.
16 pp, 2004.
[2] Stable sets of periodic solutions of a delay differential equation.
14 pp, 1995, to appear in Proceedings of the International Conference on Differential Equations Marrakesh 1995.
[1]

with J. Mallet-Paret: Rapid oscillations are rare in scalar systems governed by monotone negative feedback with a time lag.
35 pp, 1994.

Articles in journals and proceedings, theses
[61] A periodic solution of a differential equation with state-dependent delay.
Journal of Differential Equations 244 (2008), 1910-1945.
[60] State-dependent delays, linearization and periodic solutions.
In Trends in Dynamical Systems, pp. 59-72, Dumortier, F., Roose, A., and A.
Vanderbauwhede eds., Koninklijke Vlaamse Academie van Belgie voor Weten-
schappen en Kunsten, Brussel, 2007.
[59] On a model for soft landing with state-dependent delay.
Journal of Dynamics and Differential Equations 19 (2007), 593-622.
[58] with F. Hartung, T. Krisztin, J. Wu: Functional differential equations with state-dependent delay: Theory and applications.
HANDBOOK OF DIFFERENTIAL EQUATIONS, Ordinary differential equations, volume 3, pp 435-545, Canada, A., Drabek., P. and A. Fonda eds., Elsevier Science B. V., North Holland, Amsterdam 2006.
[57]

Dynamics of delay differential equations.
In Delay Differential Equations and Applications, NATO Sci. Ser. II Math.
Phys. Chem., 205, pp. 411-476. Arino, O., Hbid, M. L., and E. Ait Dads eds.,
Springer, Dordrecht, 2006.
[56] with A.L. Skubachevskii: On the Floquet multipliers of periodic solutions to nonlinear functional differential equations.
Journal of Dynamics and Differential Equations 18 (2006), 257-355
[55] Bifurcation of periodic solutions with large periods for a delay differential equation.
Annali di Matematica Pura ed Applicata 185 (2006), 577-611
[54] with A.L. Skubachevskii: On hyperbolicity of solutions with irrational periods to some functional differential equations.
Doklady Akad. Nauk 402 (2005), 151-154. English version: Doklady Math. 71 (2005), 346-348.
[53] with Th. Erneux: Bifurcation to large period oscillations in physical systems controlled by delay.
Physical Review E 72 (2005), 066206(5)
[52] Convergence to square waves in a price model with delay.
Discrete and Continuous Dynamical Systems 13 (2005), 1325-1342.
[51] with A.L. Skubachevskii: On the hyperbolicity of rapidly oscillating periodic solutions to functional differential equations.
Functional Analysis and Its Applications 39 (2005), 68-70.
[50]

Smoothness properties of semiflows for differential equations with state-dependent delay.
Russian, in Proceedings of the International Conference on Differential and Functional Differential Equations Moscow 2002, vol. 1, 40-55. Moscow State Aviation Institute (MAI), Moscow 2003.
English version: Journal of the Mathematical Sciences 124 (2004), 5193-5207.

[49] with P. Brunovský and A. Erdélyi: On a model of a currency exchange rate - local stability and periodic solutions.
Journal of Dynamics and Differential Equations 16 (2004), 393-432.
[48] Stable periodic motion of a system using echo for position control.
Journal of Dynamics and Differential Equations 15 (2003), 143-223.
[47] Differentiable semiflows for differential equations with state-dependent delay.
Universitatis Iagellonicae Acta Mathematica, Fasciculus XLI (2003), 53-62.
[46] The solution manifold and $C^1$-smoothness for differential equations with state dependent delay.
Journal of Differential Equations 195 (2003), 46-65.
[45]

Stable periodic motion of a delayed spring.
Topological Methods in Nonlinear Analysis 21 (2003), 1-28.

[44] with A.L. Skubachevskii: On Floquet multipliers of slowly oscillating periodic solutions of nonlinear functional differential equations.
Trudy Moskov. Mat. Obshch. 64 (2002), 3-54; English translation in: Transactions of the Moscow Mathematical Society 2003, 1-44.
[43] with A.L. Skubachevskii: On the spectrum of the monodromy operator for slowly oscillating periodic solutions of functional differential equations.
Dokl. Acad. Nauk 384 (2002), 442-445; English translation in: Russian Acad. Sci. Math. 65 (2002).
[42] Stable periodic motion of a system with state-dependent delay.
Differential and Integral Equations 15 (2002), 923-944.
[41] Contracting return maps for monotone delayed feedback.
Discrete and Continuous Dynamical Systems 7 (2001), 259-274.
[40] Contracting return maps for some delay differential equations.
In Topics in Functional Differential and Difference Equations, T. Faria and P. Freitas eds., 349-360, Fields Institute Communications series vol. 29, A.M.S., Providence 2001.
[39]

with T. Krisztin: Unique periodic orbits for delayed positive feedback and the global attractor.
Journal of Dynamics and Differential Equations 13 (2001), 1-57.

[38] with T. Krisztin and J. Wu: The structure of an attracting set defined by delayed and monotone positive feedback.
CWI Quarterly 12 (1999), 315-327.
[37] The singularities of an attractor of a delay differential equation.
Functional Differential Equations 5 (1998), 513-548.
[36] with M. Yebdri: Smoothness of the attractor of almost all solutions of a delay differential equation.
DISSERTATIONES MATHEMATICAE CCCLXVIII (1997).
[35]

with B. Lani-Wayda: Chaotic motion generated by delayed negative feedback. Part II: Construction of nonlinearities.
Mathematische Nachrichten 180 (1996), 141-211.

[34] The two-dimensional attractor of $x'(t)=-\mu x(t)+f(x(t-1))$.
Memoirs of the A.M.S. 544 (1995).
[33] with B. Lani-Wayda: Chaotic motion generated by delayed negative feedback. Part I: A transversality criterion.
Differential and Integral Equations 8 (1995), 1407-1452.
[32] Unstable manifolds of periodic orbits of a differential delay equation.
In Oscillation and Dynamics in Delay Equations, J.R. Graef and J.K. Hale eds., 177-240, Contemporary Mathematics vol. 129, A.M.S., Providence 1992.
[31] with A.F. Ivanov and B. Lani-Wayda: Unstable hyperbolic periodic solutions of differential delay equations.
In Recent Trends in Differential Equations, R.P. Agarwal ed., 301-316, WSSIAA vol 1, World Scientific, Singapore 1992.
[30] A differential delay equation with a planar attractor.
In Proceedings of the International Conference on Differential Equations Marrakesh 1991, Université Cadi Ayyad, Marrakesh.
[29] An invariant manifold of slowly oscillating solutions for $\dot{x}(t)=-\mu x(t)+f(x(t-1))$.
Journal für die reine und angewandte Mathematik 414 (1991), 67-112.
[28] On Floquet multipliers of periodic solutions of delay equations with monotone nonlinearities.
In Proceedings of the International Symposium on Functional Differential Equations Kyoto 1990, T. Yoshizawa and J. Kato eds., 349-356, World Scientific, Singapore 1991.
[27]

with H. Steinlein: Hyperbolic sets, transversal homoclinic trajectories, and symbolic dynamics for $C^1$-maps in Banach spaces.
Journal of Dynamics and Differential Equations 2 (1990), 325-365.

[26] Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas.
DISSERTATIONES MATHEMATICAE CCXCI (1990). (Corrections in: Annales Polonici Mathematici 58 (1993), 105-106.)
[25] Hyperbolic periodic solutions, heteroclinic connections and transversal homoclinic points in autonomous differential delay equations.
Memoirs of the A.M.S. 402 (1989).
[24]

with H. Steinlein: Hyperbolic sets and shadowing for noninvertible maps.
In Advanced Topics in the Theory of Dynamical Systems, G. Fusco, M. Iannelli, and L. Salvadori eds., 219-234, Academic Press, New York 1989.

[23] Homoclinic and periodic solutions of scalar differential delay equations.
In Dynamical Systems and Ergodic Theory, Banach Center Publ. vol 23, 243-263, PWN Polish Scientific Publishers, Warsaw 1989.
[22] with S.N. Chow: Characteristic multipliers and stability of symmetric periodic solutions of $\dot{x}(t)=g(x(t-1)))$.
Transactions of the A.M.S. 307 (1988), 127-142.
[21]

Bifurcation from homoclinic to periodic solutions by an inclination lemma with pointwise estimate.
In Dynamics of Infinite Dimensional Systems, S.N. Chow and J.K. Hale eds., 458-470, Springer, New York 1987.

[20] Inclination lemmas with dominated convergence.
Journal of Applied Mathematics and Physics (ZAMP) 32 (1987), 327-337.
[19] Dynamics of feedback systems with time lag.
In Temporal Order. Proceedings of a Symposium on Oscillations in Heterogeneous Chemical and Biological Systems, L. Rensing and N.I. Jäger eds., 281-290, Springer, Heidelberg 1985.
[18] A uniqueness problem for a nonlinear differential delay equation.
In Delay Equations, Approximation and Applications, G. Meinardus and G. Nürnberger eds., 348-351, Birkhäuser, Basel 1985.
[17] Bifurcation from a heteroclinic solution in differential delay equations.
Transactions of the A.M.S. 290 (1985), 213-233.
[16] with U. an der Heiden: Chaos in differential delay equations.
In The IXth International Conference on Nonlinear Oscillations, Yu. A. Mitropolskii ed., vol. 2, 88-91, Kiev 1984.
[15] Bifurcation from periodic solutions in functional differential equations.
Mathematische Zeitschrift 182 (1983), 269-289.
[14]

with U. an der Heiden: Existence of chaos in control systems with delayed feedback.
Journal of Differential Equations 47 (1983), 273-295.

[13] Density of slowly oscillating solutions of $\dot{x}(t)=- f(x(t-1))$.
Journal of Mathematical Analysis and Applications 79 (1981), 127-140.
[12] Delay equations: Instability and the trivial fixed point's index.
In Abstract Cauchy Problems and Functional Differential Equations, F. Kappel and W. Schappacher eds., 231-238, Research Notes in Mathematics 48, Pitman, London 1981.
[11] Homoclinic solution and chaos in $\dot{x}(t)=f(x(t-1))$.
Nonlinear Analysis 5 (1981), 775-788.
[10] with U. an der Heiden and M.C. Mackey: Complex oscillations in a simple deterministic neuronal network.
In Mathematical Aspects of Physiology, F.C. Hoppensteadt ed., 355-360, A.M.S., Providence 1981.
[9]

On instability, $\omega$-limit sets, and periodic solutions of nonlinear autonomous differential delay equations.
In Functional Differential Equations and Approximation of Fixed Points, H.O. Peitgen and H.O. Walther eds., 489-503, Lecture Notes in Mathematics 730, Springer, Heidelberg 1979.

[8] A theorem on the amplitudes of periodic solutions of delay equations, with an application to bifurcation.
Journal of Differential Equations 29 (1978), 396-404.
[7]

Über Ejektivität und periodische Lösungen bei Funktionaldifferentialgleichungen mit verteilter Verzögerung.
Habilitationsschrift, München 1977.

[6]

On the eigenvalues of linear autonomous differential delay equations.
In Ordinary and Partial Differential Equations, W.N. Everitt and B.D. Sleeman eds., 513-517, Lecture Notes in Mathematics 564, Springer, Heidelberg 1976.

[5] On a transcendental equation in the stability analysis of a population growth model.
Journal of Mathematical Biology 3 (1976), 187-195.
[4] Stability of attractivity regions for autonomous functional differential equations.
Manuscripta mathematica 15 (1975), 349-363.
[3] Existence of a non-constant periodic solution of a nonlinear functional differential equation representing the growth of a single species population.
Journal of Mathematical Biology 1 (1975), 227-240.
[2] Asymptotic stability for some functional differential equations.
Proceedings of the Royal Society of Edinburgh 74 A (1974/5), 253-255.
[1] Lineare Partielle Differentialoperatoren mit kompakter Einbettung.
Doctoral dissertation, München 1974.