Vorlesungen im WS 2011/12

Analysis Dynamischer Systeme

Partielle Differentialgleichungen (Math)

Partielle Differentialgleichungen (Ing)

Informationen für ältere Semester

Mathematik für FZT, MB, MTR, OTR, LA 

Skript

J. Knobloch und J. Steigenberger
Gewöhnliche Differentialgleichungen, TU Ilmenau, 1996   (Download)

Discrete and continuous dynamical systems

• Homoclinic and heteroclinic phenomena

• Reversible and equivariant dynamics

Non-reversible perturbations of homoclinic snaking scenarios
(with M Vielitz and Th. Wagenknecht) pdf-File

Nonreversible Homoclinic Snaking
(with Th. Rieß and M Vielitz)
Dynamical Systems 26 (2011) 335-365.
 DOI: 10.1080/14689367.2011.592488

Shift dynamics near T-point heteroclinic cycles 
(with J.S.W. Lamb and K. Webster); pdf-File 

Bifurcations from codimension one relative homoclinic cycles 
 (with A.J. Homburg, A.C. Jukes and J.S.W. Lamb); 
Trans. Amer. Math. Soc. 363 (2011),  5663-5701.

Isolas of 2-pulse solutions in homoclinic snaking scenarios 
(with DJB Lloyd, B. Sandstede, and Th. Wagenknecht); 
JDDE 23 (2011) 93-114.
DOI: 10.1007/s10884-010-9195-9

Switching homoclinic networks 
(with A.J. Homburg); 
Dynamical Systems 25 (2010), 351-358.  
DOI: 10.1080/14689361003769770 

Lin's method for heteroclinic chains involving periodic orbits 
(with Th. Rieß); 
Nonlinearity 23 (2010), 23-54.  

Snakes, ladders, and isolas of localised patterns 
 (with M. Beck, DJB Lloyd, B. Sandstede, and Th. Wagenknecht);
 SIAM J. Math. Anal. Volume 41, Issue 3 (2009), 936-972. 
 DOI: 10.1137/080713306 

Saddle-nodes and period-doublings of Smale horseshoes: a case study near resonant homoclinic bellows 
(with A.J. Homburg, A.C. Jukes and J.S.W. Lamb); 
Bull. Belg. Math. Soc. Simon Stevin, 15 (2008), 833-850.  

Snaking of multiple homoclinic orbits in reversible systems 
(with Th. Wagenknecht); 
SIAM J. Appl. Dyn.. Syst. Vol.7, No. 4 (2008), 1397-1420. 

Chaotic behaviour near non-transversal homoclinic points with quadratic tangency,
JDEA 12 (2006), 1037-1057.  

Multiple homoclinic orbits in conservative and reversible systems 
(with A.J. Homburg);
 Trans. Amer. Math. Soc. 358 (2006), 1715-1740.  

Homoclinic Snaking near a Heteroclinic Cycle in Reversible Systems 
(with Th. Wagenknecht); 
Physica D: Nonlinear Phenomena, Volume 206, Issues 1-2 , 15 June 2005, pp. 82-93. 

Bellows bifurcating from degenerate homoclinic orbits in conservative systems 
(with A.J. Homburg);
EQUADIFF 2003, Proceedings, Ed. Dumortier/Broer/Mawhin/Vanderbauwhede/Lunel,
World Scientific, 2005, pp. 963-971. 

Lin`s method for discrete and continuous dynamical systems and applications
TU Ilmenau 2004; pdf-File

Bifurcation of homoclinic orbits to a saddle-center in reversible systems 
(with J. Klaus);
International Journal of Bifurcation and Chaos, Vol.13, No. 9 (2003), pp.2603-2622

Chaotic behaviour near non-transversal homoclinic points with quadratic tangency
Preprint TU Ilmenau No. M07/00 

Reduction of Hopf bifurcation problems with symmetries
Bull. Belg. Math. Soc. 7(2000), 1-11 

Lin`s method for discrete dynamical systems
Journal of Difference Equations and Applications, Vol. 6(2000), 577-623 

Jump estimates for Lin`s method
Preprint TU Ilmenau No. M31/99 

Characterization of homoclinic points bifurcating from degenerate homoclinic orbits 
(with B.Marx and M.El Morsalani)
Preprint TU Ilmenau No M13/97

Bifurcation of degenerate homoclinics in reversible and conservative systems
Journal of Dynamics and Differential Equations, Vol.9 No.3, pp. 427-444, 1997 

A general reduction method for periodic solutions in conservative and reversible systems 
(with A.Vanderbauwhede)
Journal of Dynamics and Differential Equations, Vol.8 No.1, pp.71-102, 1996 

Hopf bifurcation at k-fold resonances in conservative systems 
(with A.Vanderbauwhede)
in: Nonlinear Dynamical Systems and Chaos, Ed. Broer/van Gils/Hoveijn/Takens, Birkhäuser, 1995, pp.155-171 

Hopf bifurcation at k-fold resonances in reversible systems 
(with A.Vanderbauwhede)
Preprint TU Ilmenau No M16/95  

Homoclinic points near degenerate homoclinics in periodically forced systems 
(with U.Schalk),
Nonlinearity, Vol.8, pp. 1133-1141, 1995 

Hopf bifurcation at k-fold resonances in equivariant reversible systems 
(with A. Vanderbauwhede)
in: Dynamics, Bifurcation and Symmetry, Ed. P.Chossat, Kluwer Academic Publishers, 1993, pp. 167-181