It is well known that the average position or barycenter of generic orbits for the standard tent map is 0.5. Periodic orbits are exceptional orbits in the sense that most of them have barycenters different from 0.5. In this paper we prove that for any positive integer n, there exist n distinct periodic orbits for the standard tent map with the same barycenter. We also provide some patterns of p...

We demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge strongly influence the conduction spectrum of this resonator, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits...

Every action of a group on a set decomposes the set into orbits. The group acts on each of the orbits and an orbit does not have sub-orbits (unequal orbits are disjoint), so the decomposition of a set into orbits could be considered as a “factorization” of the set into “irreducible” pieces for the group action. Our focus here is on these irreducible parts, namely group actions with a single orbit.

We determine the admissible nilpotent coadjoint orbits of real and p-adic split exceptional groups of types G2, F4, E6 and E7. We find that all Lusztig-Spaltenstein special orbits are admissible. Moreover, there exist nonspecial admissible orbits, corresponding to “completely odd” orbits in Lusztig’s special pieces. In addition, we determine the number of, and representatives for, the non-even ...

We consider the orbits of particles with spin in the Schwarzschild spacetime. Using the PapapetrouDixon equations of motion for spinning particles, we solve for the orbits and focus on those that exhibit chaos using both Poincaré maps and Lyapunov exponents. In particular, we develop a method for comparing the Lyapunov exponents of chaotic orbits. We find chaotic orbits for smaller spin values ...

A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials Ar take the simple form (l/r) = 1 + e cos(mφ), where k = 2 − α > 0 and l and e are generalisations of the semilatus-rectum and the eccentricity. m is given as a function of ‘eccentricity’. For nearly circular orbits m is √ k, while the above orbit becomes exact at ...

An important problem in the dynamics of surface homeomorphisms is determining the forcing relation between orbits. The forcing relation between periodic orbits can be computed using standard algorithms, though this does not give much information on the structure of the forcing relation. Here we consider forcing relations between homoclinic orbits, and their relationships with periodic orbits. W...

We have performed a detailed analysis of orbital motion in the vicinity of a nearly extremal Kerr black hole. For very rapidly rotating black holes—spin parameter a J=M > 0:9524M—we have found a class of very strong-field eccentric orbits whose orbital angular momentum Lz increases with the orbit’s inclination with respect to the equatorial plane, while keeping latus rectum and eccentricity fix...

In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic orbits and their stability. Stable periodic orbits are surrounded by regular librations in phase space and in such domains the capture of trans-Neptunian obje...

The hydrogen molecule contains the basic ingredients to understand the chemical bond, i.e, a pair of electrons. We show a step to understand The Correspondence Principle for chaotic system in the Chemical World. The hydrogen molecule is studied classically as an extension of the helium atom. Several types of orbits were found for two-fixedcenters system (hydrogen molecule) starting from some kn...