Related papers: Paperfolding Structures as Templates for Horseshoe…
We analyze chaos in the well-known nonautonomous Double-Gyre system. A key focus is on folding, which is possibly the less-studied aspect of the "stretching + folding = chaos" mantra of chaotic dynamics. Despite the Double-Gyre not having…
Hierarchically designed mechanical metamaterials involve nested levels of structural organization, mimicking natural structures (such as bones, wood, and bird feathers) to create advanced functional materials. Compositional hierarchy, a…
The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two…
In this paper we study parameter families of truncated horseshoes as models of multiscattering systems which show a transition to chaos without losing hyperbolicity, so that the topological features of the transition are completely…
We present a general scheme how to construct a substitution rule for generating $d$-dimensional analogues of the paperfolding structures. This substitution is proven to be primitive, so that the translation action on the hull forms a…
We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential equations defining a flow on a three-dimensional manifold.…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
We consider the complexification of the Henon family of quadratic diffeomorphisms of the plane, and the region of parameter space corresponding to complex horseshoes. We discuss some conjectures about the global topology of the complex…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
Using X-ray tomography, we experimentally investigate the structural evolution of packings composed of 3D-printed hexapod particles, each formed by three mutually orthogonal spherocylinders, during tap-induced compaction. We identify two…
This paper enriches the topological horseshoe theory using finite subshift theory in symbolic dynamical systems, and develops an elementary framework addressing incomplete crossing and semi-horseshoes. Two illustrative examples are…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map. The action of this map can be visualized as…
Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport…
We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
Chaotic dynamics are ubiquitous in nature and useful in engineering, but their geometric design can be challenging. Here, we propose a method using reservoir computing to generate chaos with a desired shape by providing a periodic orbit as…
It is shown that applying manifold learning techniques to Poincar\'e sections of high-dimensional, chaotic dynamical systems can uncover their low-dimensional topological organization. Manifold learning provides a low-dimensional embedding…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…