Related papers: Invariant Manifolds of Complex Systems
Nontwist area-preserving maps violate the twist condition at specific orbits, resulting in shearless invariant curves that prevent chaotic transport. Plasmas and fluids with nonmonotonic equilibrium profiles may be described using nontwist…
The reduction of dimensionality of physical systems, specially in fluid dynamics, leads in many situations to nonlinear ordinary differential equations which have global invariant manifolds with algebraic expressions containing relevant…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…
We propose a hybrid physics-informed machine learning framework to approximate invariant manifolds (IMs) of discrete-time dynamical systems driven by exogenous autonomous dynamics (exosystems). Such systems appear in applications ranging…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
We investigate the integrability of 2-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular we prove unique integrability of dynamically dominated…
Invariant manifolds are of fundamental importance to the qualitative understanding of dynamical systems. In this work, we explore and extend MacKay's converse KAM condition to obtain a sufficient condition for the nonexistence of invariant…
A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…
The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in e.g. boundary layer flows. The dynamical…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…
We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does…
We undertake a systematic exploration of recurrent patterns in a 1-dimensional Kuramoto-Sivashinsky system. For a small, but already rather turbulent system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set…
As in an earlier paper we start from the hypothesis that physics on the Planck scale should be described by means of concepts taken from ``discrete mathematics''. This goal is realized by developing a scheme being based on the dynamical…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
We examine a model of non-self-avoiding, fluctuating surfaces as a candidate continuum string theory of surfaces in three dimensions. This model describes Dynamically Triangulated Random Surfaces embedded in three dimensions with an…