Related papers: Estimating topological entropy from the motion of …
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at…
Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland et al. [P. L.…
There are many industrial situations where rods are used to stir a fluid, or where rods repeatedly stretch a material such as bread dough or taffy. The goal in these applications is to stretch either material lines (in a fluid) or the…
We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or…
Stirring of fluid with moving rods is necessary in many practical applications to achieve homogeneity. These rods are topological obstacles that force stretching of fluid elements. The resulting stretching and folding is commonly observed…
Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…
Topologically chaotic fluid advection is examined in two-dimensional flows with either or both directions spatially periodic. Topological chaos is created by driving flow with moving stirrers whose trajectories are chosen to form various…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
Topological entropy serves as a viable candidate for quantifying mixing and complexity of a highly chaotic system. Particularly in turbulence, this is determined as the exponential stretching rate of a fluid material line that typically…
There are several physical situations in which the `tangling' of a loop is relevant: the game of cat's cradle is a simple example, but a more important application involves the stirring of a fluid by rods. Here we discuss how elementary…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
In 2004, Manning showed that the topological entropy of the geodesic flow for a surface of negative curvature decreases as the metric evolves under the normalised Ricci flow. It is an interesting open problem, also due to Manning, to…
In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…
In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure…
We study the mobility of extended objects (rods) on a spherical liquid-liquid interface to show how this quantity is modified in a striking manner by both the curvature and the topology of the interface. We present theoretical calculations…
The topological entanglement entropy is used to measure long-range quantum correlations in the ground state of topological phases. Here we obtain closed form expressions for topological entropy of (2+1)- and (3+1)-dimensional loop gas…
Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with…