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Introduction to Applied Nonlinear Dynamical Systems and Chaos
Equilibrium Solutions, Stability, and Linearized Stability * Liapunov Functions * Invariant Manifolds: Linear and Nonlinear Systems * Periodic Orbits * Vector Fields Possessing an Integral * Index
Normally Hyperbolic Invariant Manifolds in Dynamical Systems
In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally
Chaotic transport in dynamical systems
Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space
An analytical study of transport, mixing and chaos in an unsteady vortical flow
We examine the transport properties of a particular two-dimensional, inviscid incompressible flow using dynamical systems techniques. The velocity field is time periodic and consists of the field
Geometric Structures, Lobe Dynamics, and Lagrangian Transport in Flows with Aperiodic Time-Dependence, with Applications to Rossby Wave Flow
Summary. In this paper we develop the mathematical framework for studying transport in two-dimensional flows with aperiodic time dependence from the geometrical point of view of dynamical systems
Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach
Steadily Translating Waves and Meanders.- Integrability of Lagrangian Motion.- Fluctuating Waves and Meanders.- Material Manifolds, Flow Regimes, and Fluid Exchange.- Lobe Transport and Flux.-
The dynamical systems approach to lagrangian transport in oceanic flows
▪ Abstract Chaotic advection and, more generally, ideas from dynamical systems, have been fruitfully applied to a diverse, and varied, collection of mixing and transport problems arising in
On the integrability and perturbation of three-dimensional fluid flows with symmetry
SummaryThe purpose of this paper is to develop analytical methods for studyingparticle paths in a class of three-dimensional incompressible fluid flows. In this paper we study three-dimensionalvolume
Periodic orbits in slowly varying oscillators
We develop a global perturbation technique for the study of periodic orbits in three-dimensional, time dependent and independent, perturbations of planar Hamiltonian differential equations. We give...