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Nekhoroshev stability for the D’Alembert problem of Celestial Mechanics

Luca Biasco, Luigi Chierchia (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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.

New algebras of functions on topological groups arising from G-spaces

E. Glasner, M. Megrelishvili (2008)

Fundamenta Mathematicae

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 spectral multiplicities for ergodic actions

Anton V. Solomko (2012)

Studia Mathematica

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 U T of G defined in L²(X,μ) ⊖ ℂ by U T ( g ) f : = f T - g . 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.

Hector Giacomini, Malick Ndiaye (1996)

Publicacions Matemàtiques

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’s method over global height fields

Xander Faber, Adam Towsley (2014)

Journal de Théorie des Nombres de Bordeaux

For any field K 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 f K x will succeed in finding some root of f in the v -adic topology for infinitely many places v of K . Furthermore, we show that if K 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 v -adically...

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