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Prof. Dr. Achim Ilchmann

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Jürgen Knobloch

Telefon: 03677 69 3250
03677 69 3270
Curiebau, Weimarer Straße 25, Zimmer 221
  TU Ilmenau
                         Postfach 10 05 65  
                         98684 Ilmenau


Lehrveranstaltungen im WS 2019/20

Analysis I

Partielle Differentialgleichungen (Math)     

Informationen für ältere Semester 

Partielle Differentialgleichungen (Ing.)   


J. Knobloch und J. Steigenberger
Gewöhnliche Differentialgleichungen, TU Ilmenau, 1996


Discrete and continuous dynamical systems

  • Homoclinic and heteroclinic phenomena
  • Reversible and equivariant dynamics



A model equation for the creation of shift dynamics in reversible systems

Shift dynamics near non-elementary T-points with real eigenvalues
(with J.S.W. Lamb and K.N. Websterpdf-file      
Journal of Difference Equations and Applications (GDEA) 24 (2018), pp. 609-654
Published online: 01 Jun 2017
DOI: 10.1080/10236198.2017.1331890

Non-conservative perturbations of homoclinic snaking scenarios
(with M. Vielitz) 
Final version published online: 22-OCT-2015
Journal of Differential Equations 260 (2016), pp. 517-566
DOI: 10.1016/j.jde.2015.09.005
Until December 11, 2015 free download available:

Using Lin's method to solve Bykov's Problems 
(with J.S.W. Lamb and K.N. Websterpdf-file  
Journal of Differential Equations 257 (2014) 2984-3047
DOI: 10.1016/j.jde.2014.06.006

Construction of codimension one homoclinic cycles 
(with A.J. Homburg and M. Kellnerpdf-file  
Dyn. Syst. 29 (2014) , No. 1, 133-151  

Non-reversible perturbations of homoclinic snaking scenarios
(with M Vielitz and Th. Wagenknecht)
Nonlinearity 25 (2012) 3469–3485

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

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 LloydB. 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. BeckDJB LloydB. 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