Arbeitsgruppe Prof. Dr. Fritz Colonius - Kontrolltheorie

Tobias Gayer

• On Markov chains and the spectra of the corresponding Frobenius-Perron operators. Stoch. Dyn. 1 (2001), no. 4, 477-491.
• Control sets and their boundaries under parameter variation. J. Differential Equations 201 (2004), no. 1, 177–200.
• Controllability and invariance properties of time-periodic systems. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 15 (2005), no. 4, 1361–1375.
• mit Fritz Colonius und Iakovos Matsikis: Numerical computation of invariant densities of linear control systems driven by multiplicative white noise. Internat. J. Control 78 (2005), no. 10, 734–746.
• mit Fritz Colonius und Wolfgang Kliemann: Near invariance for Markov diffusion systems. SIAM J. Appl. Dyn. Syst. 7 (2008), no. 1, 79–107.

Isabell Graf

• Boundaries of local no-return sets for control systems. J. Dyn. Control Syst. 17 (2011), no. 3, 311–328.

Stefan Grünvogel

• The Lyapunov spectrum of blockdiagonal semilinear control systems. J. Dynam. Control Systems 4 (1998), no. 2, 191–216.
• Bifurcation of control sets at singular points. International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999), 853–855, World Sci. Publ., River Edge, NJ, 2000.
• Lyapunov exponents and control sets near singular points. J. Differential Equations 187 (2003), no. 2, 201-225.

Christoph Kawan

• On expanding maps and topological conjugacy. J. Difference Equ. Appl. 13 (2007), no. 8-9, 803–820.
• mit Torben Stender: Lipschitz conjugacy of linear flows. J. Lond. Math. Soc. (2) 80 (2009), no. 3, 699–715.
• mit Fritz Colonius: Invariance entropy for control systems. SIAM J. Control Optim. 48 (2009), no. 3, 1701–1721.
• Upper and lower estimates for invariance entropy. Discrete Contin. Dyn. Syst. 30 (2011), no. 1, 169-186.
• mit Fritz Colonius: Invariance entropy for outputs. Math. Control Signals Systems 22 (2011), no. 3, 203-227.
• Invariance entropy of control sets, SIAM J. Control Optim. 49 (2011), no. 2, 732-751.
• Lower bounds for the strict invariance entropy, Nonlinearity 24 (2011), no. 7, 1910-1936.

Albert Marquardt

• mit Fritz Colonius, Edwin Kreuzer und Wolfgang Sichermann: A numerical study of capsizing: comparing control set analysis and Melnikov's method. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 18 (2008), no. 5, 1503–1514.

Martin Rasmussen

• Morse decompositions of nonautonomous dynamical systems. Trans. Amer. Math. Soc. 359 (2007), no. 10, 5091–5115.
• Attractivity and bifurcation for nonautonomous dynamical systems. Lecture Notes in Mathematics, 1907. Springer, Berlin, 2007.
• Nonautonomous bifurcation patterns for one-dimensional differential equations. J. Differential Equations 234 (2007), no. 1, 267-288.
• mit Fritz Colonius und Peter Kloeden: Morse spectrum for nonautonomous differential equations. Stoch. Dyn. 8 (2008), no. 3, 351-363.
• All-time Morse decompositions of linear nonautonomous dynamical systems. Proc. Amer. Math. Soc. 136 (2008), no. 3, 1045–1055.
• mit Fritz Colonius und Thorsten Hüls: Connecting orbits in perturbed systems. Nonlinear Dynam. 59 (2010), no. 4, 569–578.

Torben Stender

• A generalization of imaginary parts of eigenvalues for matrices: chain rotation numbers. Linear Algebra Appl. 426 (2007), no. 1, 53-70.
• mit Christoph Kawan: Lipschitz conjugacy of linear flows. J. Lond. Math. Soc. (2) 80 (2009), no. 3, 699–715.

Dietmar Szolnoki

• Viability kernels and control sets. ESAIM Control Optim. Calc. Var. 5 (2000), 175-185.
• Set oriented methods for computing reachable sets and control sets. Discrete Contin. Dyn. Syst. Ser. B 3 (2003), no. 3, 361-382.

Tobias Wichtrey

• mit Fritz Colonius: Control systems with almost periodic excitations. SIAM J. Control Optim. 48 (2009), no. 2, 1055–1079.