Thursday, June 24, 2004

Research Update


Ditching Bio for a while,
also ditching Control Theory for a while.

Trying to read Nikolai Makarov's work on the thermodynamics of rational maps.
I don't know what this is, either.
A "pressure spectrum" P(t) is defined for a rational map F.
I don't understand why it is important. However, P(t) is related to "certain transfer operators."
Some keywords in this work:
Analytic, i.e. under certain conditions given in paper, the negative spectrum is real analytic
Rational functions
Riemann sphere, Spherical metric
Critical points, Periodic Points, i.e. limit sets of the dynamical system

More general:
Complex Dynamics
Conformal Dynamical Systems

I will try to ignore the portions relating to "measure" and dimension spectra, since I haven't studied measure theory. I ran away from Ma 110b in January.

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