[PDF] Top 20 Periodic Orbits with Least Period Three on the Circle

... Because of 1, it is well known that a map on the interval must have periodic points of each least period if it has a periodic point of least period 3. This result was actually a ... See full document

... unit circle: either a FM = 1, or a FM = − 1, or there is a pair of complex conjugate FMs with unit ...assumed periodic boundary conditions in the original PDEs, we expect the spectrum of the linearization ... See full document

... treated three examples that arise in convection problems: PWs in two dimensions, and APWs and ARs in three ...unit circle together; this degeneracy can lead to drifting solutions, as in the numerical ... See full document

... Sun-Earth three-body problem, while little research has been conducted to investigate the potential of solar sailing in the Earth-Moon three-body ...sail periodic orbits in the Earth-Moon ... See full document

... isolated periodic orbits [10, 11] (see also ...involves three periodic orbits whose action differences all increase with the same power of the parameter that describes the distance to ... See full document

... The Newton method starts with an orbit X (t) initialized at t = 0 on a surface of section. In our case we require that the orbit be exactly 1 year so the return map in the rotating-pulsating frame is defined by a T-map ... See full document

... of periodic orbits in Sun-Mars and Sun-Earth systems are analyzed using Poincare surface of section technique and the effects of oblateness of smaller primary on these orbits are ...on period, ... See full document

... The Newton method starts with an orbit X(t) initialized at t = 0 on a surface of section. In our case we require that the orbit be exactly 1 year so the return map in the rotating-pulsating frame is defined by a T-map of ... See full document

... the periodic orbits around stable triangular equilibrium points when the three participating bodies are modeled as oblate spheroids, under effect of, radiation of the main masses and small change in ... See full document

... of orbits is obtained and illus- trated in ...All three orbits are ...green orbits, the period decreases with the increase of energy probably due to the crossing of the bi- furcation ... See full document

... small periodic motions generated by Lagrangian solutions for all values of μ and for small values of h for which the conditions of holomorphic integral theorem are ...of periodic orbits from the ... See full document

... any periodic solution of the solar sail ERTBP must have a period which is an integer multiple of 1 ...applications periodic orbits of one year are most convenient for remote sensing of the ... See full document

... non-Keplerian orbits, such as closed orbits displaced high above the ecliptic plane (see McInnes, 1 Waters and McInnes, 2 Simo and McInnes 3 ...non-Keplerian orbits, since they can apply a propulsive ... See full document

... stable periodic orbit through a fold (saddle-node ...stable periodic orbit gradually loses stability and then becomes unstable as it ‘turns around’ at the fold ...of periodic or- bits, meaning that ... See full document

... the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted ... See full document

... been carried out on the collinear libration points by considering the oblateness of one or two primaries for the circular restricted three-body problem. Sharma and Subbarao [3] investigated the the locations of ... See full document

... in equations (.)-(.) satisfies  T f (x(t))x (t) dt = , which is crucial for obtaining an a priori bounds of all the possible T -periodic solutions for equation (.)-equation (.). However, the first order ... See full document

... Lyapunov orbits, thus we include some notes on computation methods. Periodic Lyapunov orbits can be computed using a high order an- alytic expansion (see Llibre, Martinez and Sim´ o [1985]) or by ... See full document

... (1) As a restriction, [7] guarantees only one periodic solution, also the value of | µ | may be very small; but by Theorem 4.2, we obtain many periodic so- lutions. Moreover, we have no restriction for | µ ... See full document

... Since the Jacobi constant can be obtained at each libration point, then this enables to obtain the zero-velocity curves about each point. Since the variation of parameter solution of Equation (25) gives expressions for ... See full document