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Scattering monodromy and the A 1 singularity

100%
Bates L., Cushman R.
Open Mathematics
|
2007
|
tom 5
|
nr 3
429-451
EN
We present the notion of scattering monodromy for a two degree of freedom hyperbolic oscillator and apply this idea to determine the Picard-Lefschetz monodromy of the isolated singular point of a quadratic function of two complex variables.
2
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On a property of weak resolvents and its application to a spectral problem

61%
Uetake Y.
Annales Polonici Mathematici
|
1997
|
tom 66
|
nr 1
263-268
EN
We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.
3
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Well-posed linear systems - a survey with emphasis on conservative systems

51%
Weiss G., Staffans O. J., Tucsnak M.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 1
7-33
EN
We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space. We give results about the stability, controllability and observability of such conservative systems and illustrate these with a system modeling a controlled beam.
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