Related papers: Space of initial values of a map with a quartic in…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
We give a definition of mass for conformally compactifiable initial data sets. The asymptotic conditions are compatible with existence of gravitational radiation, and the compactifications are allowed to be polyhomogeneous. We show that the…
In this paper we perform the analysis that leads to the space of initial conditions for the Hamiltonian system $q' = p^2 + zq + \alpha$, $p' = -q^2 - zp - \beta$, studied by the author in an earlier article. By compactifying the phase space…
Let $k$ be a field, let $G$ be a reductive group, and let $V$ be a linear representation of $G$. Let $V//G = Spec(Sym(V^*))^G$ denote the geometric quotient and let $\pi: V \to V//G$ denote the quotient map. Arithmetic invariant theory…
We formulate the initial value problem for causal variational principles in the continuous setting on a compact metric space. The existence and uniqueness of solutions is analyzed. The results are illustrated by simple examples.
We classify noninvertible, holomorphic selfmaps of the projective plane that preserve an algebraic web. In doing so, we obtain interesting examples of critically finite maps.
Some aspects of phase transitions can be more conveniently studied in the orbit space of the action of the symmetry group. After a brief review of the fundamental ideas of this approach, I shall concentrate on the mathematical aspect and…
We establish a sufficient condition for a continuous map, acting on a compact metric space, to have a Baire residual set of points exhibiting historic behavior (also known as irregular points). This criterion applies, for instance, to a…
We introduce a compact moduli scheme of marked noncommutative cubic surfaces as the GIT moduli scheme of relations of a quiver associated with a full strong exceptional collection on a cubic surface. It is a toric variety containing the…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
We construct a lot of K3 surface automorphisms of positive entropy having rotation domains of ranks 1 and 2. To carry out this construction, we first lay theoretical foundations concerning equivariant linearization of nonlinear maps under…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
The topological entropy of a continuous self-map of a compact metric space can be defined in several distinct ways; when the space is not assumed compact, these definitions can lead to distinct invariants. The original, purely topological…
We show that there exist real quadratic maps of the interval whose attractors are computationally intractable. This is the first known class of such natural examples.
We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.
We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of discontinuities and of non-degenerate critical points and/or singular points with infinite derivative, and satisfy…
We explain how the disparate kinematics of quantum mechanics (finite-dimensional Hilbert space of QM) and special relativity (Minkowski spacetime from the Lorentz transformations of SR) can both be based on one principle (relativity…
The suspicion that the existence of a minimal uncertainty in position measurements violates Lorentz invariance seems unfounded. It is shown that the existence of such a nonzero minimal uncertainty in position is not only consistent with…
In this paper, some particular rational maps P_n ---> P_n+1, called quadratic congruences, are studied. They appear in the theory of exceptional vector bundles on projective spaces.