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1.
A general direct method, alternative to KAM theory, apt to deal with small divisor problems in the real-analytic category, is presented and tested on several small divisor problems including the construction of maximal quasi-periodic solutions for nearly-integrable non-degenerate Hamiltonian or Lagrangian systems and the construction of lower dimensional resonant tori for nearly-integrable Hamiltonian systems. The method is based on an explicit graph theoretical representation of the formal power series solutions, which allows to prove compensations among the monomials forming such representation.L.C. thanks C. Simó and theCentre de Recerca Matemàtica (Bellaterra) for kind hospitality; he also acknowledges partial support by CNR-GNAFA. The authors gratefully acknowledge helpful discussions with C. Liverani. 相似文献
2.
A result by J. N. Mather on the non-uniqueness of solutions of Percival's Euler-Lagrange equations for invariant sets of a certain class of area-preserving twist homeomorphisms of the cylinder is extended and made quantitative. As a by-product a new criterion for the non-existence of invariant circles is found.This work has been completed while the author was a guest of the ETH, Theoretische Physik, Zürich. 相似文献
3.
L. Chierchia 《Regular and Chaotic Dynamics》2008,13(2):130-139
Following closely Kolmogorov’s original paper [1], we give a complete proof of his celebrated Theorem on perturbations of
integrable Hamiltonian systems by including few “straightforward” estimates.
相似文献
4.
Alessandra Celletti Luigi Chierchia 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,57(1):33-41
A new (iso-energetic) KAM method is tested on a specific three-body problem “extracted” from the Solar system (Sun-Jupiter
+ asteroid 12 Victoria). Analytical results in agreement with the observed data are established. This paper is a concise presentation
of [2].
Supported by the MIUR projects: “Dynamical Systems: Classical, Quantum, Stochastic” and “Variational Methods and Nonlinear
Differential Equations”
Received: February 3, 2004 相似文献
5.
Matteo Chierchia Peilin Xu Gabriel J. Lovinger James P. Morken 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2019,131(40):14383-14387
A hybrid transition‐metal/radical process is described that results in the addition of organozinc reagents and alkyl halides across alkenyl boron reagents in an enantioselective catalytic fashion. The reaction can be accomplished both intermolecularly and intramolecularly, providing useful product yields and high enantioselectivities in both manifolds. 相似文献
6.
One-parameter families of area-preserving twist maps of the formF
(x, y)=(x +y +f(x),y +f(x)) are considered. Various invariant curves, for the maps corresponding tof(x)=sin andf(x)=sinx+(1/50) sin(5x), are rigorously constructed forlarge values of the nonlinearity parameter . For larger values of , close to critical, some numerical experiments are briefly discussed. 相似文献
7.
A. Berretti A. Celletti L. Chierchia C. Falcolini 《Journal of statistical physics》1992,66(5-6):1613-1630
We consider KAM invariant curves for generalizations of the standard map of the form (x, y)=(x+y, y+f(x)), wheref(x) is an odd trigonometric polynomial. We study numerically their analytic properties by a Padé approximant method applied to the function which conjugates the dynamics to a rotation +. In the complex plane, natural boundaries of different shapes are found. In the complex plane the analyticity region appears to be a strip bounded by a natural boundary, whose width tends linearly to 0 as tends to the critical value. 相似文献
8.
L. Chierchia C. Falcolini 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(2):210-220
We extend a recent method of proof of a theorem by Kolmogorov on the conservation of quasi-periodic motion in Hamiltonian systems so as to prove existence of (uncountably many) real-analytic quasi-periodic solutions for elliptic systems u=f
x
(u, y), whereu y
M
u(y)
N
,f=f(x, y) is a real-analytic periodic function and is a small parameter. Kolmogorov's theorem is obtained (in a special case) whenM=1 while the caseN=1 is (a special case of) a theorem by J. Moser on minimal foliations of codimension 1 on a torusT
M
+1. In the autonomous case,f=f(x), the above result holds for any . 相似文献
9.
A class of analytic (possibly) time-dependent Hamiltonian systems withd degrees of freedom and the corresponding class of area-preserving, twist diffeomorphisms of the plane are considered. Implementing a recent scheme due to Moser, Salamon and Zehnder, we provide a method that allows us to construct explicitly KAM surfaces and, hence, to give lower bounds on their breakdown thresholds. We, then, apply this method to the HamiltonianHy
2/2+(cosx+cos(x–t)) and to the map (y,x)(y+ sinx,x+y+ sinx) obtaining, with the aid of computer-assisted estimations, explicit approximations (within an error of 10–5) of the golden-mean KAM surfaces for complex values of with || less or equal than, respectively, 0.015 and 0.65. (The experimental numerical values at which such surfaces are expected to disappear are about, respectively, 0.027 and 0.97.) A possible connection between break-down thresholds and singularities in the complex -plane is pointed out.To our friend and colleague Paola CalderoniSupported by Consiglio Nazionale delle Ricerche, Italy 相似文献
10.
Woohyung Jeon Ramil Baiazitov Matteo Chierchia Kyle Niederer Hongyu Ren Young-Choon Moon Bradley B. Gilbert 《Helvetica chimica acta》2023,106(9):e202300091
A variety of di- and trifluoromethyl-s-triazines are prepared following straightforward synthetic protocols from simple, commercially available starting materials. Trichloromethyl-substituted triazine electrophiles are obtained in good yield and react with amine nucleophiles to afford aminotriazine products in good to excellent yield. The nucleophilic aromatic substitution reaction is broad in scope and proceeds smoothly with both aromatic and aliphatic (primary, secondary, and branched) amines in the presence of non-participating functional groups including alcohols, carboxylic acids, indoles, and common amine protecting groups. Furthermore, most reactions require only a catalytic amount of 4-DMAP with no stoichiometric base and are complete within two hours at ambient temperature. 相似文献