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1.
Antoni Ferragut Jaume Llibre Marco Antonio Teixeira 《Rendiconti del Circolo Matematico di Palermo》2007,56(1):101-115
We studyC
1 perturbations of a reversible polynomial differential system of degree 4 in. We introduce the concept of strongly reversible vector field. If the perturbation is strongly reversible, the dynamics of
the perturbed system does not change. For non-strongly reversible perturbations we prove the existence of an arbitrary number
of symmetric periodic orbits. Additionally, we provide a polynomial vector field of degree 4 in with infinitely many limit cycles in a bounded domain if a generic assumption is satisfied.
The first two authors are partially supported by a MCYT grant number MTM2005-06098-C02-01, and by a CICYT grant number 2005SGR
00550. The second author is partially supported by a FAPESP-BRAZIL grant 10246-2. All authors are also supported by the joint
project CAPES-MECD grant HBP2003-0017. 相似文献
2.
M. Taghavi 《Rendiconti del Circolo Matematico di Palermo》1999,48(2):237-242
The quotient of
divided by
, whereP is a self-inversive and unimodular polynomial of any degree, dominates an absolute constantK>1. A 1989 paper gaveK=1.0252 on which its authors conjetured that the best constant is
. We supply counter examples to their claim and provide a partial result for whenever theL
q norm is replaced by some “discrete” type norm.
Research supported by the Shiraz University Grant 72-SC-784-432. 相似文献
3.
Joan C. Artés Jaume Llibre Nicolae Vulpe 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):417-444
A quadratic polynomial differential system can be identified with a single point of through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems
of having a rational first integral of degree 2. We show that there are only 24 topologically different phase portraits in the
Poincaré disc associated to this family of quadratic systems up to a reversal of the sense of their orbits, and we provide
a unique representative of every class modulo an affine change of variables and a rescalling of the time variable. Moreover,
each one of these 24 representatives is determined by a set of invariant conditions and each respective first integral is
given in invariant form directly in
The authors are partially supported by a MEC/FEDER grant MTM2005-06098-C02-01, and a CONACIT grant number 2005SGR-00550.
Partially supported by CRDF-MRDA CERIM-1006-06 相似文献
4.
A. El Kinani 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):369-380
We consider the space, where Ω is a family of weights. We give a sufficient condition, on Ω, for to be locally convex algebra with continuous multiplication. Examples of such weights are also provided. 相似文献
5.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2000,49(1):115-120
Let
be a sequence of positive numbers and 1 ≤p < ∞. We consider the spacel
P(β) of all power series
such that
. We give a necessary and sufficient condition for a polynomial to be cyclic inl
P(β) and a point to be bounded point evaluation onl
P(β). 相似文献
6.
In this paper we investigate a class of Lie group actions on
, the so-calledpolar actions, that naturally generalize the standard
actions. For a domain invariant under such an action (i.e., a generalized Reinhardt domain) we characterize the invariant
plurisubharmonic functions and determine the envelope of holomorphy in geometric terms. For a generalized Reinhardt domain
containing the origin of
we also compute its automorphism group.
Supported in part by NSF Grant 8602020 相似文献
7.
Ivan Č. Jovanović Eberhard Malkowsky Vladimir Rakočević 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):308-314
LetF be aBK space withAK and
denote the set of all formal power series
with
such that
ε F for the sequence of coefficients of
. We give a necessary and sufficient condition for a point to be a bounded point evaluation on
, and for a polynomial to be cyclic in
. As special cases, we obtain the results for the space ℓ
p
(β) in [7].
Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and,
in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8. 相似文献
8.
Summary Quaternion generalized fiber bundles
are studied, both isomorphic to global tensorial product
ordinary quaternion fiber bundles right and left respectively) and quite general ones. A cohomology class
is considered which represents the obstruction in order the fiber bundle be a tensorial product. Several properties and a
splitting principle are proved for bundles
. On this ground and founding on a convenient bundle BE → X associated to jaz (that we call Bonan's bundle and for which ɛ(
=ɛ(BE)) relations are stated among Stiefel-Whitney classes of
, BE and the class ɛ.
Entrata in Redazione il 14 agosto 1974.
Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni. 相似文献
Entrata in Redazione il 14 agosto 1974.
Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni. 相似文献
9.
L. I. Danilov 《Mathematical Notes》1997,61(1):48-57
We consider Stepanov almost periodic functions μ ∈
ranging in the metric space
of Borel probability measures on a complete separable metric space
is equipped with the Prokhorov metric). The main result is as follows: a function
, belongs to
if and only if for each bounded continuous function
, the function
is Stepanov almost periodic (of order 1) and
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 57–68, January, 1997.
Translated by I. P. Zvyagin 相似文献
10.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2002,51(3):403-410
Let
be a sequence of positive numbers and 1≤p<∞. We consider the spaceH
p(β) of all power series
such that Σ|
(n)|p β(n
p<∞. We investigate regions on which our formal power series represent bounded analytic functions.
Research partially supported by the Shiraz University Research Council Grant No. 79-SC-1311-675. 相似文献
11.
In this paper we extend the Darboux theory of integrability in ℝ
n
to the regular algebraic hypersurfaces. Then we apply the extended theory first to the 3-dimensional generalized cylinders
×ℝ3−r
of ℝ4 forr=0, 1, 2, 3; and after to then-dimensional sphere
of ℝ
n+1. 相似文献
12.
The defect relation for holomorphic maps
in respect to slowly moving target hyperplanes in
is proved. The sharp defect boundn+1 is obtained.
Communicated by Yoram Sagher 相似文献
13.
Moshe Dubiner 《Journal d'Analyse Mathématique》1995,67(1):39-116
We consider the problem of polynomial approximation to a real valued functionf defined on a compact set
. An approximation theorem is proven in terms of the newly defined modulus of approximation. It is shown to imply a multidimensional
Jackson type theorem which is stronger than previously known results even for the interval [−1, 1]. A strong multidimensional
Bernstein type inverse theorem is also proven. We allow quite general approximation quasi-norms including
for 0<q≤∞.
We have found that the space of polynomials ℙ on a compact setX induces a semimetric
which encapsulates the local structure of ℙ. Any semimetric ρ equivalent to
suffices for the rough theory presented here. Many examples of sets
and their metrics are presented. 相似文献
14.
For a positive integer n and R>0, we set
. Given R>1 and n≥4 we construct a sequence of analytic perturbations (H
j
) of the completely integrable Hamiltonian
on
, with unstable orbits for which we can estimate the time of drift in the action space. These functions H
j
are analytic on a fixed complex neighborhood V of
, and setting
the time of drift of these orbits is smaller than (C(1/ɛ
j
)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly resonant surface, the result is therefore almost optimal since the stability
exponent for such orbits is 1/2(n−2). An analogous result for Hamiltonian diffeomorphisms is also proved. Two main ingredients are used in order to deal with
the analytic setting: a version of Sternberg's conjugacy theorem in a neighborhood of a normally hyperbolic manifold in a
symplectic system, for which we give a complete (and seemingly new) proof; and Easton windowing method that allow us to approximately
localize the wandering orbits and estimate their speed of drift. 相似文献
15.
V. M. Petrogradsky 《Israel Journal of Mathematics》1999,113(1):323-339
Suppose that
% MathType!End!2!1! is a variety of Lie algebras, and letc
n(
% MathType!End!2!1!) be the dimension of the linear span of all multilinear words onn distinct letters in the free algebraF(
% MathType!End!2!1!,X) of the variety
% MathType!End!2!1!. We consider an exponential generating function
% MathType!End!2!1!, called the complexity function. The complexity function is an entire function of a complex variable provided
the variety of Lie algebras is nontrivial. In this paper we introduce the notion of complexity for Lie varieties in terms
of the growth of complexity functions; also we describe what the complexity means for the codimension growth of the variety.
Our main goal is to specify the complexity of a product of two Lie varieties in terms of the complexities of multiplicands.
The main observation here is thatC(
% MathType!End!2!1!),z) behaves like a composition of three functionsC(
% MathType!End!2!1!),z), exp(z), andC(
% MathType!End!2!1!),z).
Partially supported by grant RFFI 96-01-00146; the author is grateful to the University of Bielefeld for hospitality, where
he was DAAD-fellow. 相似文献
16.
17.
Résumé Dans un célèbre papier ([3]), B. GIDAS et J.SPRUCK ont utilisé-sous des hypothèses adéquates- la technique du “blow up” pour
montrer que les solutionsu ∈C
0
∩C
1 (Ω) du problème
admettent une estimation a priori dansC
0
.
Dans ce travail, on montre que, si les solutionsu sont juste supposéesC
0
, une telle estimation a priori n’existe plus.
In a famous paper ([3]), B. GIDAS and J. SPRUCK used a “blow-up” argument to show that, under appropriate assumptions, all
the solutionsu ∈C
0
∩C
1 (Ω) of the problem
admit an a priori estimate inC
0
.
In this work, we show that, if one supposes the solutions are only inC
0
, such an a priori estimate does not hold. 相似文献
18.
V. L. Oleînik 《Journal of Mathematical Sciences》2000,101(3):3133-3138
Let {
}, where {
} is the open unit disk on the complex plane {
}. In G, we consider analytic solutions u(t, z) ({
}, {
}) of the heat equation 2ut=uzz with initial data f(z)=u(0, z) belonging to the Fock space F, i.e., to the space of entire functions square summable with
the weight e−|z|2.Conditions on a nonnegative measure μ on G are described under which for all f ∈ F we have {
} Bibliography: 17 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 146–155.
Translated by S. V. Kislyakov. 相似文献
19.
20.
Let
denote the closed subspace of
consisting of analytic functions in the unit disk
. For certain class of subharmonic
, the Hankel operatorH
b on
with symbol
is studied. Criteria for boundedness and compactness of such kind of Hankel operators are presented.R. Rochberg's research was partially supported by a grant from the National Science Foundation. 相似文献