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621.
This work is a generalization of the method proposed in [I.A. García, S. Maza, Linearization of analytic isochronous centers from a given commutator, J. Math. Anal. Appl. 339 (1) (2008) 740-745] of linearization of analytic isochronous centers from a given commutator. In this paper we propose a constructive procedure to get the change of variables that orbitally linearizes a smooth planar vector field on C2 around an elementary singular point (i.e., a singular point with associated eigenvalues λ,μ∈C satisfying λ≠0) or a nilpotent singular point from a given infinitesimal generator of a Lie symmetry. 相似文献
622.
For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. We study using analytic tools the dynamics of such system. We describe its global dynamics near the infinity, and prove that it has no Darboux first integrals. 相似文献
623.
Ryszard Kutner Jaume Masoliver 《The European Physical Journal B - Condensed Matter and Complex Systems》2017,90(3):50
In this article we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism, the numerous modifications permitted by its flexibility, its various applications, and the promising perspectives in the various fields of knowledge. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We focused on a pivotal role of CTRWs mainly in anomalous stochastic processes discovered in physics and beyond. This article plays the role of an extended announcement of the Eur. Phys. J. B Special Issue [http://epjb.epj.org/open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on] containing articles which show incredible possibilities of the CTRWs. 相似文献
624.
Nonlinear Dynamics - For a $$C^{m+1}$$ differential system on $$\mathbb {R}^n$$ , we study the limit cycles that can bifurcate from a zero–Hopf singularity, i.e., from a singularity with... 相似文献
625.
We analyse the existence of symmetric periodic orbits of the two-electron atom. The results obtained show that there exist six families of periodic orbits that can be prolonged from a continuum of periodic symmetric orbits. The main technique applied in this study is the continuation method of Poincaré. 相似文献
626.
627.
Dr. Judith Oró-Solé Dr. Ignasi Fina Dr. Carlos Frontera Dr. Jaume Gàzquez Dr. Clemens Ritter Marina Cunquero Dr. Pablo Loza-Alvarez Dr. Sergio Conejeros Prof. Pere Alemany Prof. Enric Canadell Prof. Josep Fontcuberta Prof. Amparo Fuertes 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2020,132(42):18553-18557
Non-centrosymmetric polar compounds have important technological properties. Reported perovskite oxynitrides show centrosymmetric structures, and for some of them high permittivities have been observed and ascribed to local dipoles induced by partial order of nitride and oxide. Reported here is the first hexagonal perovskite oxynitride BaWON2, which shows a polar 6H polytype. Synchrotron X-ray and neutron powder diffraction, and annular bright-field in scanning transmission electron microscopy indicate that it crystalizes in the non-centrosymmetric space group P63mc, with a total order of nitride and oxide at two distinct coordination environments in cubic and hexagonal packed BaX3 layers. A synergetic second-order Jahn–Teller effect, supported by first principle calculations, anion order, and electrostatic repulsions between W6+ cations, induce large distortions at two inequivalent face-sharing octahedra that lead to long-range ordered dipoles and spontaneous polarization along the c axis. The new oxynitride is a semiconductor with a band gap of 1.1 eV and a large permittivity. 相似文献
628.
Jaume Llibre Regilene Oliveira Claudia Valls 《Journal of Nonlinear Mathematical Physics》2017,24(4):473-494
In 2011 Pehlivan proposed a three–dimensional forced–damped autonomous differential system which can display simultaneously unbounded and chaotic solutions. This untypical phenomenon has been studied recently by several authors. In this paper we study the opposite to its chaotic motion, i.e. its integrability, mainly the existence of polynomial, rational and Darboux first integrals through the analysis of its invariant algebraic surfaces and its exponential factors. 相似文献
629.
Joan C. Artés Jaume Llibre Nicolae Vulpe 《Rendiconti del Circolo Matematico di Palermo》2010,59(3):419-449
A quadratic polynomial differential systemcan be identified with a single point of ?12 through its coefficients. The phase portrait of the quadratic systems having a rational first integral of degree 3 have been studied using normal forms. Here using the algebraic invariant theory, we characterize all the non-degenerate quadratic polynomial differential systems in ?12 having a rational first integral of degree 3. We show that there are only 31 different topological 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 representatives of every class modulo an affine change of variables and a rescaling of the time variable. Moreover, each one of these 31 representatives is determined by a set of algebraic invariant conditions and we provide for it a first integral. 相似文献
630.
Lyapunov, Weinstein, and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory, we establish a similar result for a differential system without assuming the existence of a first integral. Our result can also be interpreted as a kind of special Hopf bifurcation. © 2010 Wiley Periodicals, Inc. 相似文献