Related papers: Substitution Rules for Higher-Dimensional Paperfol…
We develop a systematic approach to continuous substitutions on compact Hausdorff alphabets. Focussing on implications of irreducibility and primitivity, we highlight important features of the topological dynamics of their (generalised)…
The article presents a new perspective on the isomorphism problem for non-ergodic measure-preserving dynamical systems with discrete spectrum which is based on the connection between ergodic theory and topological dynamics constituted by…
By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have purely absolutely continuous diffraction and mixed dynamical spectrum, with absolutely continuous and pure point parts. We…
We explain and restate the results from our recent paper arXiv:1503.08000.v3 in standard language for substitutions and $S$-adic systems in symbolic dynamics. We then produce as rather direct application an $S$-adic system (with finite set…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
This is an expository paper on the dynamical properties of substitutions in propositional many-valued logics. We identify substitutions with endomorphisms of free algebras, and we study their actions on the dual spectral spaces.
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
We develop a framework based on the covariant phase space formalism that identifies gravitational edge modes as dynamical reference frames. They enable the identification of the associated spacetime region and the imposition of boundary…
To a graph, Hausel and Proudfoot associate two complex manifolds, B and D, which behave, respectively like moduli of local systems on a Riemann surface, and moduli of Higgs bundles. For instance, B is a moduli space of microlocal sheaves,…
Paper withdrawn; will be replaced by revised version containing application to lattice models as well. We study hierarchical properties of Sturmian words. These properties are similar to those of substitution dynamical systems. This…
We develop furthur the correspondence between a d+1 dimensional theory and a d dimensional one with the "radial" (d+1)th corodinate \rho playing the role of an evolution parameter. We discuss the evolution of an effective action defined on…
We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal…
The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group to analyze the connectedness of the configuration space. Although successful in two and more dimensions, this…
Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which "forces its border." One can then represent the tiling space as an inverse limit of an inflation…
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…
The deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of…
This article introduces tree substitutions as a tool to give explicit geometric representations of the dynamical systems generated by a particular set of automorphisms of the free group.
We show that the standard discrete update rule of transformer layers can be naturally interpreted as a forward Euler discretization of a continuous dynamical system. Our Transformer Flow Approximation Theorem demonstrates that, under…
Aperiodic tiling --- a form of complex global geometric structure arising through locally checkable, constant-time matching rules --- has long been closely tied to a wide range of physical, information-theoretic, and foundational…
A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…