Related papers: Symbolic partition in chaotic maps
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
The largest Lyapunov exponent is widely used to diagnose chaos in gravitational dynamics, but in mixed phase spaces and finite-N systems it does not always provide a complete description of orbital complexity and phase-space transport.…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…
We discuss Devaney chaos on compact metric spaces using a decomposition space characterized by topological nature of symbolic dynamics. A chaotic map obtained here is defined as a topologically conjugate of the chaotic map on a…
We consider a large class of 2D area-preserving diffeomorphisms that are not uniformly hyperbolic but have strong hyperbolicity properties on large regions of their phase spaces. A prime example is the Standard map. Lower bounds for…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natural framework for comparing surfaces by minimizing…
We construct a matrix model equivalent (exactly, not asymptotically), to the random plane partition model, with almost arbitrary boundary conditions. Equivalently, it is also a random matrix model for a TASEP-like process with arbitrary…
We show, using covariant Lyapunov vectors, that the tangent space of spatially-extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled "physical" modes, which…
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic…
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…
In some maps the existence of an attractor with a positive Lyapunov exponent can be proved by constructing a trapping region in phase space and an invariant expanding cone in tangent space. If this approach fails it may be possible to adapt…
Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We here analyze the performance of one algorithm for the prediction of extreme events in the two-dimensional…
Using the tools of Differential Geometry, we define a new <<fast>> chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e. "quickly") than the usual tools, like Lyapunov Characteristic Numbers…
This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with…
We introduce a universal approach for applying the partition rank method, an extension of Tao's slice rank polynomial method, to tensors that are not diagonal. This is accomplished by generalizing Naslund's distinctness indicator to what we…
A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique…
We describe a rigorous and efficient computer algorithm for building a model of the dynamics of a polynomial diffeomorphism of C^2 on its chain recurrent set, and for sorting points into approximate chain transitive components. Further, we…