Bifurcation Theory and its applications

Bifurcation Theory and its applications

Semester
SoSe 2018

Lecturer
Nobuhiko Otoba, Bernd Ammann, Karsten Bohlen

Type of course (Veranstaltungsart)
Vorlesung

Contents
As can be explained by a logistic model with harvesting, if you catch too much fish of a particular kind from the ocean, then this species would eventually become extinct. This change from sustainable to unsustainable harvesting can be seen as a prototypical example of bifurcation phenomena. In this lecture, we discuss a general theory of bifurcation in a functional-analytic setting as well as its geometric and analytic applications to

one-dimensional dynamical systems (e.g. the logistic model),
nonlinear Dirac equations on spin manifolds,
Einstein equations in general relativity,
second-order semilinear PDEs in the Euclidean space, and
the Yamabe problem in conformal geometry,

depending on the audience interest.

Literature
[1] Hansjörg Kielhöfer, Variationsrechnung, Wiesbaden: Vieweg+Teubner, 2010.
[2] Hansjörg Kielhöfer, Bifurcation theory, second ed., Springer, 2012.

Recommended previous knowledge
Analysis I-IV, Functional analysis, basic knowledge on partial differential equations (e.g. as obtained in the lecture on the Yamabe problem)

Time/Date
Thursday 10-12

Location
M102

Course homepage
http://homepages.uni-regensburg.de/~otn30980/bifurcation
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Oral examination (without grade): Duration: 30 minutes, Date: to be arranged

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 minutes, Date: to be arranged, re-exam: Date:

Regelungen bei Studienbeginn vor WS 2015 / 16

Benotet:
- O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
Unbenotet:
- O. g. Studienleistung und Bestehen der o. g. Prüfungsleistung

Modules
BV, MV, MGAGeo, MAngAn

ECTS
3