Showing papers in "Journal of The Mathematical Society of Japan in 1985"

Lorenz attractors do not have the pseudo-orbit tracing property

Abstract: On etudie la condition sous laquelle les attracteurs de Lorenz geometriques ont la propriete de tracage de pseudo-orbite

Lp-estimates of solutions of some nonlinear degenerate diffusion equations

Abstract: On montre l'existence, l'unicite et des estimations L p des solutions globales de certaines equations de diffusion non lineaires degenerees

On integral transformations associated with a certain Lagrangian-as a prototype of quantization

Abstract: Soit M une variete de dimension finie et soit L(γ,γ˙) une fonction sur le fibre tangent TM. On construit un C 0 ―semi-groupe d'operateurs lineaires bornes H t λ(L) associes a L(γ,γ˙) et son generateur infinitesimal Aλ(L) sur l'espace de Hilbert intrinseque #7B-H(M), ou t∈R + et λ est un parametre positif

On a conformally invariant functional of the space of Riemannian metrics

Abstract: main subject in this paper is to determine inf {v(g) ; g E 1} , which will be denoted by v(M). A little consideration shows that v(M) > 0 if some Pontrjagin number of M is not zero. Thus, in general, v(M) is a nontrivial invariant of a manifold. In § 2, we shall show two general properties of v(M). One is that v(M)=0 for the total space M of a principal circle bundle (Theorem 2.1). This provides examples of M for which v(M)=0 but which has no conformally flat metric. The other is an inequality for connected sum ; v(M1#M2) <_ v(Ml)+v(M2) (Theorem 2.2). This is useful for computing v(M) for certain M. However, to determine v(M) for general M seems to be not so easy. Even for S2 X S2, (S2 x S2) is not known (to the author). We want to show that the standard Einstein metric go of S2 x S2 is a candidate at which v takes a minimum, if v : 5I(S2 x S2)--R has a minimum. In fact, go is a minimum point of v restricted to Kahler metrics (Proposition 1.4). Moreover, we shall prove that go is a strictly stable critical point of the functional v (cf. Definition 4.1 and Theorem4.2). In the course of proof of stability of go 51(S2 x S2), we establish the first and the second variational formulas of v : 5t (M) --*R for 4 dimensional M (Propositions 3.1 and 3.7; The first variational formula has already appeared in [2]). From these formulas, we can also see that other than conformally flat metrics, Einstein metrics are critical points of the functional v, and Ricci flat metrics are stable critical points of v.

Steepest descent and differential equations

Abstract: On considere la resolution numerique de problemes aux valeurs limites. On donne deux conditions. Si, pour un probleme donne elles sont satisfaites ensembles, alors la methode de plus grande pente continue contrainte converge vers une solution

Asymptotic behavior of one-dimensional random dynamical systems

Abstract: Soit S un espace mesurable et soit {τ s } s∈S une famille de transformations de l'intervalle unite I dans lui-meme non singulieres par rapport a la mesure de Lebesque m sur I. Etant donnee une transformation conservant la mesure τ et une variable aleatoire a valeur dans S: ζ sur un espace de probabilite (Ω, #7B-F, P), on considere un modele de systeme dynamique aleatoire dont l'evolution dans le temps est donnee par x n+1 =τζ nd + d 1 (a) (x n ), pour n≥1 ou ζ n =ζoτ n−1

Propagation of chaos for the Burgers equation

Abstract: On etablit la propagation du chaos pour des processus de diffusion lies aux solutions de l'equation de Burgers

Strong topological transitivity and C * -dynamical systems

Abstract: On etudie la notion de transitivite topologique forte pour des systemes dynamiques C*. On compare a la transitivite topologique

Scattering theory by Enss' method for operator valued matrices: Dirac operator in an electric field

Abstract: On etend la methode geometrique de Enss a une classe d'operateurs differentiels dans [L 2 (R n )] m , m≥2. Cette classe inclut l'operateur de Dirac avec un champ electrique dans [L 2 (R 3 )] 4

Calculation of the class numbers and fundamental units of abelian extensions over imaginary quadratic fields from approximate values of elliptic units

Abstract: 0.1. Any number field we consider is a finite extension of the rational number field $Q$ in the complex number field $C$ . Let $L/F$ be an abelian extension of number fields. For $L$ , denote its class number by $h$ and its group of units by $E$ . We restrict our study to either of the following cases: CASE 1. $F=Q$ and $L$ is contained in the real number field $R$ . CASE 2. $F$ is an imaginary quadratic number field. In this paper, we give a general procedure to calculate $h$ and to find together fundamental units of $L$ . We first connect $h$ to a finite index subgroup $E$ of $E$ by an index formula of the form $h=c(E:E)$ (Theorem 2 below). Hence $c(\\in Q)$ is rather easy to know and $E$ is generated by cyclotomic (Case 1) or so called elliptic (Case 2) units. The process to decide $(E:E)$ starts from the generators of $E$ , and ends at a free basis of $E$ (Algorithm 4 below). Thus $h$ and, at a time, fundamental units are obtained. To make the process effective, an upper bound of $(E:E)$ should be known beforehand. So we majorize $(E:E)$ by using the generators of $E$ (Theorem 3). Our method will be computer implementable, though we do not discuss it in detail. What we emphasize is that the classical (explicit) theory of cyclotomic fields or complex multiplication offers us a new general way of calculating $h$ and

The first eigenvalue of Laplacians on minimal surfaces in S 3

Abstract: On construit une famille a un parametre de surfaces rotationnelles completes dans S 3 a courbure moyenne constante