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math.NA2011
Computing the Invariant Measure and the Lyapunov Exponent for One-Dimensional Maps using a Measure-Preserving Polynomial Basis
Philip J. Aston, Oliver Junge
We consider a generalisation of Ulam's method for approximating invariant densities of one-dimensional chaotic maps. Rather than use piecewise constant polynomials to approximate t…
math.NA2011★ 87 cited
Estimating long term behavior of flows without trajectory integration: the infinitesimal generator approach
Gary Froyland, Oliver Junge, Péter Koltai
The long-term distributions of trajectories of a flow are described by invariant densities, i.e. fixed points of an associated transfer operator. In addition, global slowly mixing…