5 papers
Smooth Persistence of Attractors for Set-Valued Dynamical Systems: A Boundary Map Approach
K. Kourliouros, J. S. W. Lamb, M. Rasmussen +3
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamic…
The conditioned Lyapunov spectrum for random dynamical systems
Matheus M. Castro, Dennis Chemnitz, Hugo Chu +3
We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned…
On Boundaries of -neighbourhoods of Planar Sets, Part II: Global Structure and Curvature
Jeroen S. W. Lamb, Martin Rasmussen, Kalle Timperi
We study the global topological structure and smoothness of the boundaries of -neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x, E) \leq \v…
On Boundaries of -neighbourhoods of Planar Sets: Singularities, Global Structure, and Curvature
Jeroen S. W. Lamb, Martin Rasmussen, Kalle G. Timperi
We study the geometry, topological properties and smoothness of the boundaries of closed -neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x,…
A Girsanov approach to slow parameterizing manifolds in the presence of noise
Mickaël D. Chekroun, Jeroen S. W. Lamb, Christian J. Pangerl +1
This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exh…