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“Towards
the global bifurcation theory on the plane “
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Date: |
Download-files: |
Time: |
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Wednesday, 27. April 2016 |
Audio-only-Recording as MP3-File
(smallest possible size):
- Audio.mp3 (ca.25 Mb)
=========================================== Video-Recording for any system with MP4-support:
- Video.mp4 (ca.228 Mb) |
15:15 – 16:15 |
Speaker :
Yulij Ilyashenko (Cornell Univ, Indep. Univ
of
Abstract:
The talk
provides a new perspective of the global bifurcation theory on the plane.
Theory of
planar bifurcations consists of three parts: local, nonlocal and global ones.
It is now
clear that the latter one is yet to be created.
Local
bifurcation theory (in what follows we will talk about the plane only)
is
related to transfigurations of phase portraits of differential equations near
their singular points.
This theory
is almost completed, though recently new open problems occurred.
Nonlocal
theory is related to bifurcations of separatrix
polygons (polycycles).
Though in
the last 30 years there were obtained many new results, this theory is far from
being completed.
Recently it
was discovered that nonlocal theory contains another substantial part: a global
theory.
New
phenomena are related with appearance of the so called sparkling saddle
connections.
The aim of
the talk is to give an outline of the new theory and discuss numerous open
problems.
The main
new results are: existence of an open set of structurally unstable families of
planar vector fields,
and of
families having functional invariants (joint results with Kudryashov
and Schurov).
Thirty
years ago
bifurcation
theory in the plane. All these conjectures are now disproved. Though the theory
develops
in quite
a different direction, this development is motivated by the