Jürgen Knobloch
Telefon: 03677 69 3250
Fax: 03677 69 3270
E-Mail: juergen.knobloch@tu-ilmenau.de
Büro: Curiebau, Weimarer Straße 25, Zimmer 221
Postadresse: TU Ilmenau
Postfach 10 05 65
98684 Ilmenau
Lehre
Lehrveranstaltungen im WS 2019/20
Analysis I
Partielle Differentialgleichungen (Math)
Informationen für ältere Semester
Partielle Differentialgleichungen (Ing.)
Skript
J. Knobloch und J. Steigenberger
Gewöhnliche Differentialgleichungen, TU Ilmenau, 1996 (Download)
Forschung
Discrete and continuous dynamical systems
- Homoclinic and heteroclinic phenomena
- Reversible and equivariant dynamics
Publikationen
Publikationen
A model equation for the creation of shift dynamics in reversible systems
pdf-file
Shift dynamics near non-elementary T-points with real eigenvalues
(with J.S.W. Lamb and K.N. Webster) pdf-file
Journal of Difference Equations and Applications (GDEA) 24 (2018), pp. 609-654
Published online: 01 Jun 2017 http://dx.doi.org/10.1080/10236198.2017.1331890
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:
http://authors.elsevier.com/a/1RvtY50j-R5~n
Using Lin's method to solve Bykov's Problems
(with J.S.W. Lamb and K.N. Webster) pdf-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. Kellner) pdf-file
Dyn. Syst. 29 (2014) , No. 1, 133-151
DOI:10.1080/14689367.2013.860085
Non-reversible perturbations of homoclinic snaking scenarios
(with M Vielitz and Th. Wagenknecht)
Nonlinearity 25 (2012) 3469–3485
DOI:10.1088/0951-7715/25/12/3469
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 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