We investigate the natural families of periodic orbits associated with the equilibrium configurations of the the planar restricted 1 + n body problem for the case 2 6 n 6 4 equal mass satellites. Such periodic orbits can be used to model both trojan exoplanetary systems and parking orbits for captured asteroids within the solar system. For n = 2 there are two families of periodic orbits associa...

In this paper, we first establish the Bott-type iteration formulas and some abstract precise iteration formulas of the Maslov-type index theory associated with a Lagrangian subspace for symplectic paths. As an application, we prove that there exist at least [ n 2 ] + 1 geometrically distinct brake orbits on every C compact convex symmetric hypersurface Σ in R satisfying the reversible condition...

Bars in galaxies are mainly supported by particles trapped around stable periodic orbits. These orbits represent oscillatory motion with only one frequency, which is the bar driving frequency, and miss free oscillations. We show that a similar situation takes place in double bars: particles get trapped around parent orbits, which in this case represent oscillatory motion with two frequencies of...

[1] A quantitative analysis of thermal orbits is developed and applied to modeled air and ground temperatures. Thermal orbits are phase-space representations of air and ground temperature relationships that are generated by plotting daily or monthly ground temperatures against air temperatures. Thermal orbits are useful descriptive tools that provide straightforward illustrations of air and gro...

We study the bound states of brane/antibrane systems by examining the motion of a probe antibrane moving in the background fields of N source branes. The classical system resembles the point-particle central force problem, and the orbits can be solved by quadrature. Generically the antibrane has orbits which are not closed on themselves. An important special case occurs for some Dp-branes movin...

In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xn = f(n− 1, xn−k). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p gcd(p,k) periodic...

This paper presents a new unified theory of orbits homoclinic to resonance bands in a class of near-integrable dissipative systems. It describes three sets of conditions, each of which implies the existence of homoclinic or heteroclinic orbits that connect equilibria or periodic orbits in a resonance band. These homoclinic and heteroclinic orbits are born under a given small dissipative perturb...

0960-0779/$ see front matter 2011 Elsevier Ltd doi:10.1016/j.chaos.2011.08.002 ⇑ Corresponding author. Tel.: +55 (11) 3091 6842 6706. E-mail address: [email protected] (E.S. Medeiros). In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak h...

Gutzwiller's trace formula allows interpretation of the density of states of a classically chaotic quantum system in terms of classical periodic orbits. It diverges when periodic orbits undergo bifurcations and must be replaced with a uniform approximation in the vicinity of the bifurcations. As a characteristic feature, these approximations require the inclusion of complex ``ghost orbits''. By...

We consider the stability properties of spatial and temporal periodic orbits of one-dimensional coupled-map lattices. The stability matrices for them are of the block-circulant form. This helps us to reduce the problem of stability of spatially periodic orbits to the smaller orbits corresponding to the building blocks of spatial periodicity, enabling us to obtain the conditions for stability in...