On the mechanics with noncontinuous hamiltonians
On the minimal action function of autonomous lagrangians associated to magnetic fields
On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus
We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham’s proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus to , the minimum dilatation is the smallest Salem number for polynomials of degree .
On the mobility and efficiency of mechanical systems
It is shown that self-locomotion is possible for a body in Euclidian space, provided its dynamics corresponds to a non-quadratic Hamiltonian, and that the body contains at least 3 particles. The efficiency of the driver of such a system is defined. The existence of an optimal (most efficient) driver is proved.
On the Morse Complex.
On the mulitplier of a repelling fixed point.
On the multiplicity of brake orbits and homoclinics in Riemannian manifolds
Let be a complete Riemannian manifold, an open subset whose closure is diffeomorphic to an annulus. If is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in starting orthogonally to one connected component of and arriving orthogonally onto the other one. The results given in [5] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating...
On the nonlinear theory of micromorphic thermoelastic solids.
On the normality of arithmetical constants.
On The Notions of Mating
The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations between the polynomials and their matings are discussed and proved. Finally holomorphic motion properties of slow-mating are proved.
On the number of Arnoux-Rauzy words
On the Number of Partitions of an Integer in the -bonacci Base
For each we consider the -bonacci numbers defined by for and for When these are the usual Fibonacci numbers. Every positive integer may be expressed as a sum of distinct -bonacci numbers in one or more different ways. Let be the number of partitions of as a sum of distinct -bonacci numbers. Using a theorem of Fine and Wilf, we obtain a formula for involving sums of binomial coefficients modulo In addition we show that this formula may be used to determine the number of partitions...
On the number of places of convergence for Newton’s method over number fields
Let be a polynomial of degree at least 2 with coefficients in a number field , let be a sufficiently general element of , and let be a root of . We give precise conditions under which Newton iteration, started at the point , converges -adically to the root for infinitely many places of . As a corollary we show that if is irreducible over of degree at least 3, then Newton iteration converges -adically to any given root of for infinitely many places . We also conjecture that...
On the one class of hyperbolic systems.
On the optimal control of implicit systems
On the optimal control of implicit systems
In this paper we consider the well-known implicit Lagrange problem: find a trajectory solution of an underdetermined implicit differential equation, satisfying some boundary conditions and which is a minimum of the integral of a Lagrangian. In the tangent bundle of the surrounding manifold X, we define the geometric framework of q-pi- submanifold. This is an extension of the geometric framework of pi- submanifold, defined by Rabier and Rheinboldt for determined implicit differential equations,...
On the optimal target of a macroeconomic growth model.
On the optimality of double-bracket flows.
On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors
We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations...
On the Periodic Points of Topological Markov Chains.