Publikationen

Monographien

[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

 

[6] Delay differential equations with differentiable solution operators on open domains in
$C((−1, 0],\mathbb{R}^n)$, and processes for Volterra integro-differential equations.
25 pp, 2016.

[5]  Fréchet differentiability in Fréchet spaces, and differential equations with unbounded variable delay.
45 pp, 2016.

[4] Autonomous linear neutral equations with bounded Borel functions as initial data. 44 pp, 2010.

[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.

 

Veröffentlichungen in Zeitschriften und Tagungsbänden, Habilitationsschrift, Doktorarbeit

 

[79] with M. C. Mackey and M. Tyran-Kaminska: Response of an oscillatory differential delay equation to a single stimulus.
DOI 10.1007/s00285-016-1051-z
Journal of Mathematical Biology, to appear.

[78] Local invariant manifolds for delay dierential equations with state space in $C^1((-∞, 0], \mathbb{R}^n)$.
DOI 10.14232/ejqtde.2016.1.85
Electronical Journal of the Qualitative Theory of Differential Equations, 2016, No. 85, 1 - 29.

[77] Semiflows for differential equations with locally bounded delay on solution manifolds in the space $C^1((-\infty, 0], \mathbb{R}^n)$.
Topological Methods in Nonlinear Analysis, to appear.

[76] Merging homoclinic solutions due to state-dependent delay.
DOI 10.1016/j.jde.2015.02.009,
Journal of Differential Equations, to appear.

[75] with B. Lani-Wayda: A Shilnikov phenomenon due to state-dependent delay, by means of the fixed point index.
DOI 10.1007/s10884-014-9420-z, 
Journal of Dynamics and Differential Equations, to appear.

[74] Topics in delay differential equations.
DOI 101365/s13291-014-0086-6,
Jahresbericht der Deutschen Mathematiker-Vereinigung 116 (2014), 87-114.

[73] with M. V. Barbarossa: Linearized stability for a new class of neutral equations with state-dependent delay.
DOI 10.007/s12591-014-0204-z,
Differential Equations and Dynamical Systems, to appear.

[72] Complicated histories close to a homoclinic loop generated by variable delay.
Advances in Differential Equations 19 (2014), 911-946.

[71] A homoclinic loop generated by variable delay.
DOI 10.1007/s10884-013-9333-2,
Journal of Dynamics and Differential Equations (27) (2015), 1101-1139

[70] Evolution systems for differential equations with variable time lags. (Russian).
In Proceedings of the Sixth International Conference on Differential and Functional Differential Equations, Moscow, August 14 - 21, 2011, Part 4, Contemporary Mathematics. Fundamental Directions 48 (2013), 5 - 26.
English Version: DOI 10.1007/s10958-014-2086-6,
Journal of Mathematical Sciences.

[69] On Poisson's state-dependent delay.
Discrete and Continuous Dynamical Systems - Series A, 33 (2013), 365 - 379.

[68] Semiflows for neutral equations with state-dependent delays.
Fields Institute Communications, 64 (2013), 211 - 267.

[67] Differential equations with locally bounded delay.
Journal of Differential Equations 252 (2012), 3001 - 3039.

[66] with M. C. Mackey and M. Tyran-Kaminska: The mathematical legacy of Andrzej Lasota.
Wiadomosci Matematyczne 48 (2012), 143-156.

[65] More on linearized stability for neutral equations with state-dependent delay.
Differential Equations and Dynamical Systems 19 (2011), 315-333.

[64] Linearized stability for semiflows generated by a class of neutral equations, with applications to state-dependent delays.
Journal of Dynamics and Differential Equations 22 (2010), 439-462.

[63] with R. Qesmi: Center-stable manifolds for differential equations with state-dependent delay.
Discrete and Continuous Dynamical Systems 23 (2009), 1009-1033.

[62] Algebraic-delay differential systems, state-dependent delay, and temporal order of reactions.
Journal of Dynamics and Differential Equations 21 (2009), 195-232.

[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 -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 -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, -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.