Zheng, Jiguang

English

In this thesis, we applied tools of algebraic analysis and knowledge of
symplectic geometry and contact geometry to give a normal form of certain
class of microdifferential operators, and then studied analytic singularities
of solutions with the advantage of normal form. The microdifferential
operators are of real analytic coefficients, real principal symbols and
simple characteristics near radial points. We linearized the contact vector
fields with real analytic coefficients, classified the radial points and find an
exact normal form of our operators.
In the last two chapters, by restricting our discussion in the space of
Fourier hyperfunctions, first we fully studied the analytic singularities in
two dimensional case, and gave some estimates of singularities in higher
dimensional cases. Roughly, near an attracting (resp. repelling) generic
radial point, we can found solutions with minimal analytic singularity,
i.e. the radial direction. Furthermore, near a non-attracting (resp.
non-repelling) radial point, if the radial direction is contained in analytic
wavefront set of the solution, then either the intersection of analytic
wavefront set with stable manifold or with unstable manifold is non-empty.
Moreover we discussed solution with prescribed singularities and gave
a description of propagation of analytic singularities, especially in three
dimensional case

eDiss Georg-August-University Göttingen

Analytic singularities near radial points

https://ediss.uni-goettingen.de/bitstream/11858/00-1735-0000-0022-5F7C-2/1/Dissertation1.pdf

Analytic singularities near radial points

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eDiss Georg-August-University Göttingen