Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations.
Neimark-Sacker bifurcation in a discrete-time financial system.
Nekhoroshev estimates for quasi-convex hamiltonian systems.
Nekhoroshev stability for the D’Alembert problem of Celestial Mechanics
The classical D’Alembert Hamiltonian model for a rotational oblate planet revolving near a «day-year» resonance around a fixed star on a Keplerian ellipse is considered. Notwithstanding the strong degeneracies of the model, stability results a là Nekhoroshev (i.e. for times which are exponentially long in the perturbative parameters) for the angular momentum of the planet hold.
Neumann system and hyperelliptic functions.
New algebras of functions on topological groups arising from G-spaces
For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. We show that SUC(G) contains the algebra WAP(G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and Asplund functions respectively. For the Polish groups of order preserving homeomorphisms of the unit interval and of isometries of the Urysohn space of diameter 1, we show that SUC(G) is trivial. We introduce the notion of fixed point on a class...
New criteria for canonical number systems
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.