New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
New exact traveling wave solutions for compound KdV-Burgers equations in mathematical physics.
New explicit and exact solutions for the Nizhnik-Novikov-Vesselov equation.
New feedback functions for synchronizing chaotic maps.
New improved exponential stability criteria for discrete-time neural networks with time-varying delay.
New links and reductions between the Brockett nonholonomic integrator and related systems.
New solitons and periodic solutions for Thekadomtsev-Petviashvili equation.
New spectral multiplicities for ergodic actions
Let G be a locally compact second countable Abelian group. Given a measure preserving action T of G on a standard probability space (X,μ), let ℳ (T) denote the set of essential values of the spectral multiplicity function of the Koopman representation of G defined in L²(X,μ) ⊖ ℂ by . If G is either a discrete countable Abelian group or ℝⁿ, n ≥ 1, it is shown that the sets of the form p,q,pq, p,q,r,pq,pr,qr,pqr etc. or any multiplicative (and additive) subsemigroup of ℕ are realizable as ℳ (T)...
New sufficient conditions for a center and global phase portraits for polynomial systems.
In this paper we consider cubic polynomial systems of the form: x' = y + P(x, y), y' = −x + Q(x, y), where P and Q are polynomials of degree 3 without linear part. If M(x, y) is an integrating factor of the system, we propose its reciprocal V (x, y) = 1 / M(x,y) as a linear function of certain coefficients of the system. We find in this way several new sets of sufficient conditions for a center. The resulting integrating factors are of Darboux type and the first integrals are in the Liouville form.By...
Newton, Chebyshev, and Halley Basins of Attraction; A Complete Geometric Approach
Newton's method for solutions of quasi-Bessel differential equations.
Newton’s method over global height fields
For any field equipped with a set of pairwise inequivalent absolute values satisfying a product formula, we completely describe the conditions under which Newton’s method applied to a squarefree polynomial will succeed in finding some root of in the -adic topology for infinitely many places of . Furthermore, we show that if is a finite extension of the rationals or of the rational function field over a finite field, then the Newton approximation sequence fails to converge -adically...
Nielsen fixed point theory and symplectic Floer homology
We describe a connection between Nielsen fixed point theory and symplectic Floer homology for surfaces. A new asymptotic invariant of symplectic origin is defined.
Nielsen number is a knot invariant
We show that the Nielsen number is a knot invariant via representation variety.
Nielsen zeta function, 3-manifolds, and asymptotic expansions in Nielsen theory.
Nilpotent and recursive flows.
Nilsystèmes d’ordre 2 et parallélépipèdes
En topologie dynamique, une famille classique de systèmes est celle formée par les rotations minimales. La classe des nilsystèmes et de leurs limites projectives en est une extension naturelle. L’étude de ces systèmes est ancienne mais connaît actuellement un renouveau à cause de ses applications, à la fois à la théorie ergodique et en théorie additive des nombres. Les rotations minimales sont caractérisées par le fait que la relation de proximalité régionale est l’égalité. Nous introduisons une...
Noether theorem and first integrals of constrained Lagrangean systems
The dynamics of singular Lagrangean systems is described by a distribution the rank of which is greater than one and may be non-constant. Consequently, these systems possess two kinds of conserved functions, namely, functions which are constant along extremals (constants of the motion), and functions which are constant on integral manifolds of the corresponding distribution (first integrals). It is known that with the help of the (First) Noether theorem one gets constants of the motion. In this...
Nombre de rotation, mesures invariantes et ratio set des homéomorphismes affines par morceaux du cercle
Etant donné irrationnel de type constant, nous donnons des conditions explicites et génériques sur les pentes d’un homéomorphisme affine par morceaux du cercle de nombre de rotation , qui garantissent que la mesure de probabilité -invariante est singulière par rapport à la mesure de Haar. Cet article contient une preuve élémentaire d’un résultat de E. Ghys et V. Sergiescu : ”le nombre de rotation d’un homéomorphisme dyadique est rationnel”. Nous y étudions aussi le ratio set des homéomorphismes...
Nombre de rotation, structures géométriques sur un cercle et groupe de Bott-Virasoro
Une classification complète des stabilisateurs coadjoints du groupe de Bott-Virasoro est obtenue par une méthode essentiellement géométrique. L’outil de base est le nombre de rotation d’un difféomorphisme du cercle. En particulier, nous mettons en évidence la présence de groupes d’isotropie non-connexes et montrons que la transformation de Miura des opérateurs de Hill peut s’interpréter comme une application moment sur l’espace des structures affines du cercle.