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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 SS 2020

Analysis II

Diese Veranstaltung startet ab 20.04.2020 als Moodlekurs

Partielle Differentialgleichungen (Ing.)

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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