Related papers: Periodic behaviors
We construct a family $\{\Phi_t\}_{t\in[0,1]}$ of homeomorphisms of the two-torus isotopic to the identity, for which all of the rotation sets $\rho(\Phi_t)$ can be described explicitly. We analyze the bifurcations and typical behavior of…
We characterize charmenability among arithmetic groups and deduce dichotomy statements pertaining normal subgroups, characters, dynamics, representations and associated operator algebras. We do this by studying the stationary dynamics on…
We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite…
Given a $d$-dimensional torus map $F(z)=Mz+G(z)\bmod 1$, where $M$ is an integer-matrix and and $G$ is a periodic function, we find conditions on $M$ under which $F$ is semi-conjugate to a linear torus map, independently of $G$. We also…
We present in this communication a new solving procedure for Kelvin&Kirchhoff equations, considering the dynamics of falling the rigid rotating torus in an ideal incompressible fluid, assuming additionally the dynamical symmetry of rotation…
In this paper we study a $k$-dimensional analytic subvariety of the complex algebraic torus. We show that if its logarithmic limit set is a finite rational $(k-1)$-dimensional spherical polyhedron, then each irreducible component of the…
Nominal sets provide a framework to study key notions of syntax and semantics such as fresh names, variable binding and $\alpha$-equivalence on a conveniently abstract categorical level. Coalgebras for endofunctors on nominal sets model,…
We introduce the notion of analytic stability data on the Lie algebra of vector fields on a torus. We prove that the subspace of analytic stability data is open and closed in the topological space of all stability data. We formulate a…
The Mahler measure of a function on the real d-torus is its geometric mean over the torus. It appears in number theory, ergodic theory and other fields. The Fuglede-Kadison determinant is defined in the context of von Neumann algebra theory…
The behavior of a driven granular gas in a container consisting of $M$ connected compartments is studied employing a microscopic kinetic model. After obtaining the governing equations for the occupation numbers and the granular temperatures…
We give an explicit description of all finite Borel measures on Noetherian topological spaces X, and characterize them as objects dual to a space of functions on X. We use these results to study the asymptotic behavior of continuous…
The rational fixed point of a set functor is well-known to capture the behaviour of finite coalgebras. In this paper we consider functors on algebraic categories. For them the rational fixed point may no longer be fully abstract, i.e. a…
In this paper, we study the primitive ideals of quantum algebras supporting a rational torus action. We first prove a quantum analogue of a Theorem of Dixmier; namely, we show that the Gelfand-Kirillov dimension of primitive factors of…
Classical results due to Ingham and Paley-Wiener characterize the existence of nonzero functions supported on certain subsets of the real line in terms of the pointwise decay of the Fourier transforms. We view these results as uncertainty…
Certain objects of conformal field theory, for example partition functions on the rectangle and the torus, and one-point functions on the torus, are either invariant or transform simply under the modular group, properties which should be…
Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein's Galois…
We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's ring of real quaternions. We also characterize the generalized polynomial identities in n variables which hold over the…
We address the question of finding algebraic properties that are respectively equivalent, for a morphism between algebraic varieties over an algebraically closed field of characteristic zero, to be an homeomorphism for the Zariski topology…
We use symplectic cobordism, and the localization result of Ginzburg, Guillemin, and Karshon, to find a wall-crossing formula for the signature of regular symplectic quotients of Hamiltonian torus actions. The formula is recursive,…
Congruences of Fourier coefficients of modular forms have long been an object of central study. By comparison, the arithmetic of other expansions of modular forms, in particular Taylor expansions around points in the upper-half plane, has…