S. Jacquet. Subanalyticity of the Sub-Riemannian Distance. J. Dynam. Control Systems 5 (1999), no. 3, 303--328.
The aim of this paper is to study the subanalyticity of the distance function d defined by a sub-Riemannian structure (D , g). If the distribution is of degree 2, we prove that d is subanalytic and if D^2 is fat, d is subanalytic far away from the diagonal. In this last case we prove in fact that the function d(x_0 , \cdot ) is subanalytic in a neighborhood of x_0.
J.M. Jeong, Y.C. Kwun, and J.Y. Park. Approximate Controllability for Semilinear Retarded Functional Differential Equations. J. Dynam. Control Systems 5 (1999), no. 3, 329--346.
This paper deals with the approximate controllability of the semilinear functional differential equations with unbounded delays. We will also establish the regularity of the solution of the given system. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system by using degree theory. Finally, a simple example to which our main result can be applied is given.
I. Zelenko. Nonregular Abnormal Extremals of 2-Distribution: Existence, Second Variation, and Rigidity. J. Dynam. Control Systems 5 (1999), no. 3, 347--383.
We study existence and rigidity (W_\infty^1-isolatedness) of nonregular abnormal extremals of completely nonholonomic 2-distribution (nonregularity means that such extremals do not satisfy the strong generalized Legendre--Clebsch condition). Introducing the notion of diagonal form of the second variation, we generalize some results of A. Agrachev and A. Sarychev about rigidity of regular abnormal extremals to the nonregular case. In order to reduce the second variation to the diagonal form, we construct a special curve of Lagrangian subspaces, a Jacobi curve. We show that certain geometric properties of this curve (like simplicity) imply the rigidity of the corresponding abnormal extremal.
A.A. Prikhod'ko. Ergodic Joinings of GL(n, Z)-Action on n-Torus. J. Dynam. Control Systems 5 (1999), no. 3, 385--396.
In this paper, a classification of ergodic self-joinings of the Gl(n,Z)-action on the n-torus is given. Our study generalizes the description of the 2-fold self-joining of the Gl(2,Z)-action on Tor^2 due to K. Park. We show that any joining is a linear combination of the Haar measures on subgroups of special form.
P. Crouch, G. Kun, and F. Silva Leite. The De Casteljau Algorithm on Lie Groups and Spheres. J. Dynam. Control Systems 5 (1999), no. 3, 397--429.
We examine the De Casteljau algorithm in the context of Riemannian symmetric spaces. This algorithm, whose classical form is used to generate interpolating polynomials in R^n, was also generalized to arbitrary Riemannian manifolds by others. However, the implementation of the generalized algorithm is difficult since detailed structure, such as boundary value expressions, has not been available. Lie groups are the most simple symmetric spaces, and for these spaces we develop expressions for the first and second order derivatives of curves of arbitrary order obtained from the algorithm. As an application of this theory we consider the problem of implementing the generalized De Casteljau algorithm on an m-dimensional sphere. We are able to fully develop the algorithm for cubic splines with Hermite boundary conditions and more general boundary conditions for arbitrary m.
J.-P.Thouvenot. Weak Pinsker Joinings of Processes Satisfying the Weak Pinsker Property. J. Dynam. Control Systems 5 (1999), no. 3, 431-- 436.
We show that when two transformations satisfy the weak Pinsker property, those among their joinings which also satisfy this property are dense. In particular, the \Bar d - bar distance can be arbitrarily well approached while staying in the class.
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