Differentiable equivalence of fractional linear maps

A Moebius system is an ergodic fibred system $(B,T)$ (see \citer5) defined on an interval $B=[a,b]$ with partition (J_k),k\in I,#I\geq 2 such that $Tx=\frac{c_k+d_kx}{a_k+b_kx}$, $x\in J_k$ and $T|_{J_k}$ is a bijective map from $J_k$ onto $B$. It is well known that for #I=2 the invariant density can be written in the form $h(x)=\int_{B^*}\frac{dy}{(1+xy)^2}$ where $B^*$ is a suitable interval. This result does not hold for #I\geq 3. However, in this paper for #I=3 two classes of interval maps are determined which allow the extension of the before mentioned result.Comment: Published at http://dx.doi.org/10.1214/074921706000000257 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Dynamic Global Games of Regime Change: Learning, Multiplicity and Timing of Attacks

Global games of regime change–coordination games of incomplete information in which a status quo is abandoned once a sufficiently large fraction of agents attacks it–have been used to study crises phenomena such as currency attacks, bank runs, debt crises, and political change. We extend the static benchmark examined in the literature by allowing agents to take actions in many periods and to learn about the underlying fundamentals over time. We first provide a simple recursive algorithm for the characterization of monotone equilibria. We then show how the interaction of the knowledge that the regime survived past attacks with the arrival of information over time, or with changes in fundamentals, leads to interesting equilibrium properties. First, multiplicity may obtain under the same conditions on exogenous information that guarantee uniqueness in the static benchmark. Second, fundamentals may predict the eventual regime outcome but not the timing or the number of attacks. Finally, equilibrium dynamics can alternate between phases of tranquillity–where no attack is possible–and phases of distress–where a large attack can occur–even without changes in fundamentals.Global games, coordination, multiple equilibria, information dynamics, crises.

Langevin molecular dynamics derived from Ehrenfest dynamics

Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac-Zwanzig setting, with the initial data for the electrons stochastically perturbed from the ground state and the ratio, $M$, of nuclei and electron mass tending to infinity. The Ehrenfest nuclei dynamics is approximated by the Langevin dynamics with accuracy $o(M^{-1/2})$ on bounded time intervals and by $o(1)$ on unbounded time intervals, which makes the small $\mathcal{O}(M^{-1/2})$ friction and $o(M^{-1/2})$ diffusion terms visible. The initial electron probability distribution is a Gibbs density at low temperture, derived by a stability and consistency argument: starting with any equilibrium measure of the Ehrenfest Hamiltonian system, the initial electron distribution is sampled from the equilibrium measure conditioned on the nuclei positions, which after long time leads to the nuclei positions in a Gibbs distribution (i.e. asymptotic stability); by consistency the original equilibrium measure is then a Gibbs measure.The diffusion and friction coefficients in the Langevin equation satisfy the Einstein's fluctuation-dissipation relation.Comment: 39 pages: modeling and analysis in separate sections. Formulation of initial data simplifie

Human Center of Gravity Dynamics a New Parameter of Motor Development Functions

A study of a new parameter of human growth and development was conducted. The percentage of the height of body gravity center to the stature in supine position was measured in males and females during the period of pre-puberty (l995), young and adult puberties (1995 and 1997) and male adults (1995). The parameters measured were weight, stature and the height of the gravity center. Data were calculated in obtaining arithmetic means, standard deviations of all parameters and the percentage of gravity point height to stature. The percentages of male and female means, as well as standard deviations, were compared statistically. It was shown that in the pre-puberty group the location of the gravity center to stature was the same in percentage in males compared to females, whereas in the adult group (1987, 1995) a higher percentage was found in males. Among males (1995) differences were found in the percentages, which might have been caused by differences of body typology; the mesomorphic type showed the highest percentage, the endomorphic type showed the lowest, whereas the ectomorphic type it was in between

Dynamics of self-interacting strings and energy-momentum conservation

Classical strings coupled to a metric, a dilaton and an axion, as conceived by superstring theory, suffer from ultraviolet divergences due to self-interactions. Consequently, as in the case of radiating charged particles, the corresponding effective string dynamics cannot be derived from an action principle. We propose a fundamental principle to build this dynamics, based on local energymomentum conservation in terms of a well-defined distribution-valued energy-momentum tensor. Its continuity equation implies a finite equation of motion for self-interacting strings. The construction is carried out explicitly for strings in uniform motion in arbitrary space\u2013time dimensions, where we establish cancelations of ultraviolet divergences which parallel superstring non-renormalization theorems. The uniqueness properties of the resulting dynamics are analyzed

Arithmetic Dynamics

This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely that they (semi-) conjugate a given continuous (or measure-preserving) dynamical system and a symbolic one. The classes of dynamical systems and their codings considered in the paper involve: (1) Beta-expansions, i.e., the radix expansions in non-integer bases; (2) "Rotational" expansions which arise in the problem of encoding of irrational rotations of the circle; (3) Toral expansions which naturally appear in arithmetic symbolic codings of algebraic toral automorphisms (mostly hyperbolic). We study ergodic-theoretic and probabilistic properties of these expansions and their applications. Besides, in some cases we create "redundant" representations (those whose space of "digits" is a priori larger than necessary) and study their combinatorics.Comment: 45 pages in Latex + 3 figures in ep

Fermionic Molecular Dynamics for nuclear dynamics and thermodynamics

A new Fermionic Molecular Dynamics (FMD) model based on a Skyrme functional is proposed in this paper. After introducing the basic formalism, some first applications to nuclear structure and nuclear thermodynamics are presentedComment: 5 pages, Proceedings of the French-Japanese Symposium, September 2008. To be published in Int. J. of Mod. Phys.

Shape Dynamics

Barbour's formulation of Mach's principle requires a theory of gravity to implement local relativity of clocks, local relativity of rods and spatial covariance. It turns out that relativity of clocks and rods are mutually exclusive. General Relativity implements local relativity of clocks and spatial covariance, but not local relativity of rods. It is the purpose of this contribution to show how Shape Dynamics, a theory that is locally equivalent to General Relativity, implements local relativity of rods and spatial covariance and how a BRST formulation, which I call Doubly General Relativity, implements all of Barbour's principles.Comment: 8 pages, LaTeX, based on a talk given at Relativity and Gravitation 100 years after Einstein in Prague, June 201