Climate dynamics and fluid mechanics: Natural variability and related uncertainties

M Ghil, MD Chekroun, E Simonnet - Physica D: Nonlinear Phenomena, 2008 - Elsevier
The purpose of this review-and-research paper is twofold:(i) to review the role played in
climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding and …

Nonlinear climate dynamics: From deterministic behaviour to stochastic excitability and chaos

DV Alexandrov, IA Bashkirtseva, M Crucifix… - Physics Reports, 2021 - Elsevier
Glacial–interglacial cycles are global climatic changes which have characterized the last 3
million years. The eight latest glacial–interglacial cycles represent changes in sea level over …

[KÖNYV][B] Attractors for infinite-dimensional non-autonomous dynamical systems

A Carvalho, JA Langa, J Robinson - 2012 - books.google.com
The book treats the theory of attractors for non-autonomous dynamical systems. The aim of
the book is to give a coherent account of the current state of the theory, using the framework …

Distinguished trajectories in time dependent vector fields

JA Madrid, AM Mancho - Chaos: An Interdisciplinary Journal of …, 2009 - pubs.aip.org
We introduce a new definition of distinguished trajectory that generalizes the concepts of
fixed point and periodic orbit to aperiodic dynamical systems. This new definition is valid for …

A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: Theoretical and computational issues

AM Mancho, D Small, S Wiggins - Physics Reports, 2006 - Elsevier
In the past 15 years the framework and ideas from dynamical systems theory have been
applied to a variety of transport and mixing problems in oceanic flows. The motivation for this …

[KÖNYV][B] Attractivity and bifurcation for nonautonomous dynamical systems

M Rasmussen - 2007 - books.google.com
Although, bifurcation theory of equations with autonomous and periodic time dependence is
a major object of research in the study of dynamical systems since decades, the notion of a …

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 …

Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields

AM Mancho, D Small, S Wiggins, K Ide - Physica D: Nonlinear Phenomena, 2003 - Elsevier
In this paper, we develop two accurate and fast algorithms for the computation of the stable
and unstable manifolds of hyperbolic trajectories of two-dimensional, aperiodically time …

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

B De Saedeleer, M Crucifix, S Wieczorek - Climate Dynamics, 2013 - Springer
There is evidence that ice age cycles are paced by astronomical forcing, suggesting some
kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and …

Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system

AN Carvalho, JA Langa, JC Robinson… - Journal of Differential …, 2007 - Elsevier
In this paper we determine the exact structure of the pullback attractors in non-autonomous
problems that are perturbations of autonomous gradient systems with attractors that are the …