Related papers: The spacetime of a shift endomorphism
The vacuum structure is probed by boundary conditions. The behaviour of thermodynamical quantities like free energy, boundary entropy and entanglement entropy under the boundary renormalization group flow are analysed in 2D conformal field…
We describe the endomorphisms of the direct product of two free groups of finite rank and obtain conditions for which the subgroup of fixed points is finitely generated and we do the same for periodic points. We also describe the…
A subset of a group is characteristic if it is invariant under every automorphism of the group. We study word length in fundamental groups of closed hyperbolic surfaces with respect to characteristic generating sets consisting of a finite…
We propose that the entropy of de Sitter space can be identified with the mutual entropy of a dual conformal field theory. We argue that unitary time evolution in de Sitter space restricts the total number of excited degrees of freedom to…
We define a notion of (one-sided) edge shift spaces associated to ultragraphs. In the finite case our notion coincides with the edge shift space of a graph. In general, we show that our space is metrizable and has a countable basis of…
We discuss the entropy change due to fragmentation for black hole solutions in various dimensions. We find three different types of behavior. The entropy may decrease, increase or have a mixed behavior, characterized by the presence of a…
In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…
A survey article that presents some recent algebraic and model-theoretic results on the automorphism groups of relatively free groups of infinite rank. The topics include topological aspects, generating sets, descripition of automorpisms…
In this work, we investigate the dynamics of homeomorphisms through the lens of the local shadowing theory. We study the influence of positively shadowable points and positively shadowable measures into the local entropy theory of…
One of the few accepted dynamical foundations of non-additive "non-extensive") statistical mechanics is that the choice of the appropriate entropy functional describing a system with many degrees of freedom should reflect the rate of growth…
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
We consider a simple model of quantum disorder in two dimensions, characterized by a long-range site-to-site hopping. The system undergoes a metal-insulator transition -- its eigenfunctions change from being extended to being localized. We…
A deSitter brane-world bounding regions of anti-deSitter space has a macroscopic entropy given by one-quarter the area of the observer horizon. A proposed variant of the AdS/CFT correspondence gives a dual description of this cosmology as…
In classical spin systems with two largely different inherent time scales, the configuration of the fast spins almost instantaneously follows the slow-spin dynamics. We develop the emergent effective theory for the slow-spin degrees of…
Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…
Let $X$ be an irreducible shift of finite type (SFT) of positive entropy, and let $B_n(X)$ be its set of words of length $n$. Define a random subset $\omega$ of $B_n(X)$ by independently choosing each word from $B_n(X)$ with some…
Study of the dynamics of automorphisms of a group is usually focused on their growth and/or finite orbits, including fixed points. In this paper, we introduce properties of a different kind; using somewhat informal language, we call them…
We study the time evolution of a $3+1$ dimensional spacetime, where space is a large three-sphere, due to small perturbations of the background fields. We focus on two classes of deformations. One corresponds on the worldsheet to…