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Monthly Archives: January 2013
Spectral methods in dynamics
In the dynamics seminar here at Houston, we’re beginning a series of expository talks on statistical properties of dynamical systems. This week’s talk was given by Andrew Török and introduces some of the spectral methods for transfer operators that prove … Continue reading
More on Riccati equations and fractional linear transformations
In the last post, we saw that solutions of the nonautonomous Riccati equation are given by fractional linear transformations — that is, if is the map taking the initial condition to the solution at time , then for some functions … Continue reading
Riccati equations and fractional linear transformations
In a typical course on ordinary differential equations, the Picard–Lindelöf theorem on existence and uniqueness of solutions is followed at some point by an example illustrating that such solutions may not be defined for all time, but may go to … Continue reading