6 papers
Analytic Dependence of the Lyapunov Moment Function and the Projective Stationary Measure for Random Matrix Products
Christopher Chalhoub, Vincent P. H. Goverse, Jeroen S. W. Lamb +1
We consider the product of i.i.d. random matrices sampled according to a probability measure supported on a strongly irreducible and proximal subset of a compact set $S\subset…
-neighbourhoods in the Plane with a Nowhere-smooth Boundary
Jeroen S. W. Lamb, Martin Rasmussen, Kalle G. Timperi
We give an example of a planar set for which the boundary of its -neighbourhood $E_\varepsilon = \{x \in \mathbb{R}^2…
Anticipating bifurcations of random dynamical systems through tails of stationary densities
Wei Hao Tey, Guillermo Olicón-Méndez, Jeroen S. W. Lamb +1
We develop an early-warning signal for bifurcations of one-dimensional random difference equations with additive bounded noise, based on the asymptotic behaviour of the stationary…
Bifurcations of the Hénon map with additive bounded noise
Jeroen S. W. Lamb, Martin Rasmussen, Wei Hao Tey
We numerically study bifurcations of attractors of the Hénon map with additive bounded noise with spherical reach. The bifurcations are analysed using a finite-dimensional boundary…
Intermittent two-point dynamics at the transition to chaos for random circle endomorphisms
Vincent P. H. Goverse, Ale Jan Homburg, Jeroen S. W. Lamb
We establish the existence of intermittent two-point dynamics and infinite stationary measures for a class of random circle endomorphisms with zero Lyapunov exponent, as a dynamica…
Rigorous enclosure of Lyapunov exponents of stochastic flows
Maxime Breden, Hugo Chu, Jeroen S. W. Lamb +1
We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assis…