| 词汇 | example_english_orbit |
| 释义 | Examples of orbitThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. Qualitatively similar orbits are obtained in the many par ticle calculations. In opposition to this, chaos is effective for causing rapid desynchronization, because of its characteristic exponential divergence of nearby orbits. Dynamically we find most orbits to be stable over long time scales and typically this happens in a wider parameter area than in co-rotating systems. The bar will hence be able to relocate stars, and stars with low or high metallicity could be found far away from their original orbits. We only need that the return maps at periodic orbits are diagonal on the stable and unstable manifolds. In most cases, those planets follow orbits with significant eccentricity, leading to substantial seasonal temperature excursions. In most cases, those planets follow orbits with significant eccentricity, leading to substantial temperature excursions. Indeed, nebular drag and collisions would ensure that orbits with zero eccentricity were preferred. The steady-state solution of the equation of motion is then derived in cartesian coordinates and two groups of electron orbits are defined. Here, a planetary system consisting of one star and two identical-mass planets in circular but mutually inclined orbits is considered. Quasiperiodic orbits can look quite complicated, especially if there exist many incommensurable frequencies. The velocity of the planet orbiting at this distance satisfies the relation vn=w/n. The project mission was to locate intelligent signals coming from hypothetical planets orbiting the stars. A caustic is formed by the envelope of these orbits. Note that the orbits are almost per fectly laminar and there is no sign of filamentation. Physically, it means that diffusive particle orbits remove continuous resonance. In (2b), the term (t) allows the vertical density of the laminar orbits to change. The stability of electron orbits may be investigated as follows. Of cour se, before the present article, the effect of noise on chaotic orbits was studied, for instance, by using the standard mapping [21]. Then we have a dynamical system that could be used to establish the existence of heteroclinic orbits. The width of the transition region is very small, and orbits in this region will be scattered out on the pitch-angle scattering time scale. The static magnetic field imposes the charged particles' orbits; these orbits are perturbed by the time-dependent electromagnetic field. The particle orbits pass close to or through a region of zero magnetic field before being reflected in regions where the magnetic field is strong. One builds discreteness (of the spectrum) directly from discreteness (of periodic orbits). The ions have orbits in the magnetic field determined by their energy, the angle of injection, and the point of deposition. In this figure both the dynamic inflow and outflow of orbits can be seen. However, if the phase space contains many such saddles, it may be that typical orbits relentlessly shadow these saddles. Nearby orbits in phase space become separated due to expanding dynamics and approach each other again due to contracting dynamics. The dynamical orbits approach a fixed point, but they then escape from it. The following theorem allows us to conclude that a t -semiconformal measure is conformal provided the parabolic orbits do not mix. Moreover, the rotation has to be irrational, because the map has finitely many periodic orbits of each period. Thus, an important problem in dynamics is to understand the main mechanisms leading to the appearance of new homoclinic orbits. We prove that all of them coincide (and under an additional assumption are equal to the periodic orbits pressure). There are collision orbits left out of our symbol sequence considerations. If there are elliptic periodic orbits, can they have any period? Bounded orbits of non-quasiunipotent flows on homogeneous spaces. Section 6 proves that there are only countably many closed orbits of a certain type. In 4, we introduce a notion of orbits that generalizes the notation for dynamical systems. The flow near the sheet of symmetric periodic orbits is assumed to satisfy the following property. We want to show that the contribution of both very long and very short orbits is negliglible with respect to the previous main contribution. We can prove that for arbitrary homeomorphisms isotopic to the identity, positive asymptotic entropy forces infinitely many periodic orbits. In fact, only finitely many of these periodic orbits can generate a basin is a saddle-hyperbolic invariant set and let cell. Any system of isometries can be decomposed into minimal components and finite orbits in a certain way. One type of restriction is imposed by existence of periodic orbits. We refer to this as the ' critical-energy ' phenomenon because there seems to be a critical energy level beyond which chaotic orbits dominate the phase space. Half of the periodic orbits will be stable and half will be unstable of saddle type. The important feature which leads to chaotic advection is the breaking of heteroclinic orbits. In spite of the countable, dense set of periodic orbits, the dynamics of f are a prototype of chaotic behaviour. In some sense, which will not be explored here in detail, they correspond to homoclinic orbits in dynamical systems. If the particle orbits a t large distances are circular, then only one of these waves has non-zero amplitude. The method presented here finds only torus and iterated torus knots, because there is an obvious description of these knots through bifurcation of period-multiplying orbits. The index-theoretic methods available for detecting periodic orbits of two-dimensional self-diffeomorphisms are not sufficient for understanding general three-dimensional flows. Hence, we see that the obstructions to conjugacy cannot be local obstructions related to periodic orbits. However, from a certain dynamical perspective, this action is relatively uncomplicated (and, perhaps, uninteresting), since all of its orbits are locally closed. We can now prove the existence of non-trivial orbits. In 2, we introduce the variational setting for periodic orbits that will be used in all the following. We solve this problem and obtain, for each resonant frequency, the existence of an invariant set with homoclinic orbits. Uniformly distributed orbits of certain flows on homogeneous spaces. We show that if f is not infinitely renormalizable, then all its periodic orbits of sufficiently high period are hyperbolic repelling. Furthermore, we will see transversal heteroclinic orbits flowing from to 1 and vice versa. Moreover, if x is incommensurable, there is a natural bijection between the two orbits. However, we make no restrictions on the orbits of the critical points. Given a twist diffeomorphism f on the torus without a rotationalinvariant circle, there exist infinitely many periodic orbits with non-zero shear-rotation number. Much of the chapter is devoted to a fairly exhaustive listing of launch dates, orbits and sensor wavebands for past and current remote sensing missions. The behaviour of orbits of the critical values and asymptotic values of a function play an important role in determining the dynamics of a function. More specifically, the closure of this set of periodic orbits is in general the global attractor of the flow. Assume that both critical orbits do not tend to a periodic attractor. In this paper we investigate the problem of finding invariant measures supported on periodic orbits which approximately realize this maximum. The model's perfect-foresight dynamics allow for stable 2-, 4-, 8-, and 10-cycles, quasiperiodic orbits, and chaos. The orbits above the separatrix correspond to the motion of electrons that are out-running the wave. We focus on the study of statistical properties of orbits generated by maps, a field of research known as ergodic theory. However, this set of chaotic orbits is of measure zero. Bounded orbits of non-quasi-unipotent flows on homogeneous spaces. In these investigations the essential idea is the construction of densely wandering orbits. We propose a new classification of periodic orbits of interval maps via overrotation pairs. We claim also that p2 and p2 lie on different orbits. The next statement tells us that such symmetric orbits exist for every coupling parameter between the period doubling bifurcation point and zero. Only a finite number of periodic orbits do not satisfy (11). Accelerating orbits of twist diffeomorphisms on the torus. Under the same assumption, we prove the existence of infinitely many periodic orbits and positive entropy invariant measures with non-zero shear-rotation number. On the boundary, these diffeomorphisms are either the identity or have rational rotation number with finitely many periodic orbits. The emphasis of [20] is on elucidating the combinatorial structure of the rigid translations by coding orbits via 'even n-colourings of the integers'. The effect of square-mixing upon the presence of finite orbits is not completely understood. Also, note that when restricted to a neighborhood of 0, backward orbits approach 0 in a polynomial rate. In 4, we define normal perturbations and prove that the existence of elliptic or hyperbolic 2-periodic orbits is an open property. We will prove a quantitative estimate for the distribution of orbits. By comparing photographs obtained on slightly different orbits or times, the topography of the body is revealed. Finally, the occurrence of the bifurcation of the connecting orbits is derived from the argument above. Here are the necessary modifications, assuming the periodic orbits have positive eigenvalues. The plane in these pictures is drawn to give an idea of the movement transverse to the three characteristic orbits below the singularity. The hypothesis on the orbits can be broken into two parts for some particular flows. In our context, rigidity means that, for some systems, data at periodic orbits determine the smooth conjugacy class. Such distinct periodic orbits require distinct discontinuities of this form. Studying orbits of points of a nilmanifold under the action of a polynomial sequence of translations becomes an extremely important task. In particular, it has infinitely many closed orbits. In this context they are classically called action-minimizing orbits (and measures). Therefore, the recurrence of critical points and the growth of the derivative along their orbits play an important role in the understanding of the dynamics. Semi-hyperbolicity is even weaker, it requires that critical orbits should not be recurrent, in the absence of parabolic periodic points. There are various ways of asking for a stronger result than simply that recurrent orbits can be closed. The first is that has infinitely many periodic orbits. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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