A variational theory of hyperbolic Lagrangian coherent structures

G Haller - Physica D: Nonlinear Phenomena, 2011‏ - Elsevier
We develop a mathematical theory that clarifies the relationship between observable
Lagrangian Coherent Structures (LCSs) and invariants of the Cauchy–Green strain tensor …

A new mixing diagnostic and Gulf oil spill movement

I Mezić, S Loire, VA Fonoberov, P Hogan - Science, 2010‏ - science.org
Chaotic advection has served as the paradigm for mixing in fluid flows with simple time
dependence. Its skeletal structure is based on analysis of invariant attracting and repelling …

Distinguishing between deterministic oscillations and noise

J Rowland Adams, J Newman… - The European Physical …, 2023‏ - Springer
Time-dependent dynamics is ubiquitous in the natural world and beyond. Effectively
analysing its presence in data is essential to our ability to understand the systems from …

Finite-time Lagrangian transport analysis: stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents

M Branicki, S Wiggins - Nonlinear Processes in Geophysics, 2010‏ - npg.copernicus.org
We consider issues associated with the Lagrangian characterisation of flow structures
arising in aperiodically time-dependent vector fields that are only known on a finite time …

Hyperbolicity and invariant manifolds for planar nonautonomous systems on finite time intervals

LH Duc, S Siegmund - International Journal of Bifurcation and …, 2008‏ - World Scientific
The method of invariant manifolds was originally developed for hyperbolic rest points of
autonomous equations. It was then extended from fixed points to arbitrary solutions and from …

[ספר][B] Barriers and transport in unsteady flows: a Melnikov approach

S Balasuriya - 2016‏ - SIAM
Over the past several years, there has been an explosion of interest in analyzing flow
barriers in fluids. This has been driven by a variety of reasons. One is a concern for our …

Finite-time attractivity and bifurcation for nonautonomous differential equations

M Rasmussen - Differential Equations and Dynamical Systems, 2010‏ - Springer
The aim of this article is to introduce nonautonomous and finite-time versions of central
concepts from the theory of dynamical systems such as attractivity and bifurcation. The …

[HTML][HTML] Stabilization of cyclic processes by slowly varying forcing

J Newman, M Lucas, A Stefanovska - Chaos: An Interdisciplinary …, 2021‏ - pubs.aip.org
We introduce a new mathematical framework for the qualitative analysis of dynamical
stability, designed particularly for finite-time processes subject to slow-timescale external …

Areas of attraction for nonautonomous differential equations on finite time intervals

P Giesl, M Rasmussen - Journal of Mathematical Analysis and Applications, 2012‏ - Elsevier
In this article, new concepts of (exponential) attractivity for nonautonomous differential
equations on a finite time interval are introduced. Due to nonuniqueness of finite-time …

A definition of spectrum for differential equations on finite time

A Berger, TS Doan, S Siegmund - Journal of Differential Equations, 2009‏ - Elsevier
Hyperbolicity of an autonomous rest point is characterised by its linearization not having
eigenvalues on the imaginary axis. More generally, hyperbolicity of any solution which exists …