Related papers: Dynamics in Thompson's Group F

This paper shows that various relevant dynamical systems can be described as vector fields associated to smooth functions via a bracket that defines what we call a Leibniz structure. We show that gradient flows, some dissipative systems,…

A mixture of spin-1/2 fermionic atoms and molecules of paired fermionic atoms is studied in an optical lattice. The molecules are formed by an attractive nearest-neighbor interaction. A functional integral is constructed for this many-body…

This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian…

We study certain symplectic quotients of n-fold products of complex projective m-space by the unitary group acting diagonally. After studying nonemptiness and smoothness these quotients we construct the action-angle variables, defined on an…

We describe a Thompson-like group of homeomorphisms of the basilica Julia set. Each element of this group acts as a piecewise-linear homeomorphism of the unit circle that preserves the invariant lamination for the basilica. We develop an…

In this paper we study some aspects of thermodynamic formalism, more specifically topological pressure and, as a consequence, topological entropy for piecewise smooth vector fields, using topological conjugation with shift maps and the…

Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…

The f-invariant is an injective homomorphism from the 2-line of the Adams-Novikov spectral sequence to a group which is closely related to divided congruences of elliptic modular forms. We compute the f-invariant for two infinite families…

Let $f$ be an automorphism of a group $G$. Two elements $x, y$ in $G$ are said to be in the same $f$-twisted conjugacy class if there exists an element $z$ in $G$ such that $y=z x f(z^{-1})$. This is an equivalence relation known as…

The category of strict polynomial functors inherits an internal tensor product from the category of divided powers. To investigate this monoidal structure, we consider the category of representations of the symmetric group which admits a…

We compare two definitions of connected correlation functions in fluctuating geometries. We show results of the MC simulations for 4D dynamical triangulation in the elongated phase and compare them with the exact calculations of correlation…

We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…

Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…

Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…

We show that the modular branching rule (in the sense of Harish-Chandra) on unipotent modules for finite unitary groups is piecewise described by particular connected components of the crystal graph of well-chosen Fock spaces, under…

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…

With this paper we extend our studies [1] on polarized beams by distilling tools from the theory of principal bundles. Four major theorems are presented, one which ties invariant fields with the notion of normal form, one which allows one…

In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic…

The authors classify the finite index subgroups of R. Thompson's group $F$. All such groups that are not isomorphic to $F$ are non-split extensions of finite cyclic groups by $F$. The classification describes precisely which finite index…

We derive a framework to apply topological quantum chemistry in systems subject to magnetic flux. We start by deriving the action of spatial symmetry operators in a uniform magnetic field, which extends Zak's magnetic translation groups to…