Related papers: Grand orbit relations in wandering domains
Covering relations are a topological tool for detecting periodic orbits, symbolic dynamics and chaotic behavior for autonomous ODE. We extend the method of the covering relations onto systems with a time dependent perturbation. As an…
We apply the effective approach to evaluating semiclassical relational dynamics to the closed Friedman--Robertson--Walker cosmological model filled with a minimally coupled massive scalar field. This model is interesting for studying…
The classification of Fatou components for rational functions was concluded with Sullivan's proof of the No Wandering Domains Theorem in 1985. In 2016 it was shown, in joint work of the first and last author with Buff, Dujardin and Raissy,…
We present analytical and numerical results on integrability and transition to chaotic motion for a generalized Ziegler pendulum, a double pendulum subject to an angular elastic potential and a follower force. Several variants of the…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
It turns out that complex geodesics in Teichm\"uller spaces with respect to their invariant metrics are intrinsically connected with variational calculus for univalent functions. We describe this connection and show how geometric features…
The discovery of many giant planets in close-in orbits and the effect of planetary and stellar tides in their subsequent orbital decay have been extensively studied in the context of planetary formation and evolution theories. Planets…
The coadjoint orbit action for a multifermion system, as an exact description of its dynamics, is considered. A parametrization of the variables involved is given which facilitates the approximation of this by another coadjoint orbit action…
This work focuses on the generation of non-self-intersecting relative trajectories, and their applications to satellite constellation design, slotting architectures, and Space Traffic Management. To that end, this paper introduces two…
Motivated by the definition of super-Teichm\"uller spaces, and Penner-Zeitlin's recent extension of this definition to decorated super-Teichm\"uller space, as examples of super Riemann surfaces, we use the super Ptolemy relations to obtain…
We discuss thick domain walls interpolating between spaces with naked singularities and give arguments based on the $AdS$/CFT correspondence why such singularities may be physically meaningful. Our examples include thick domain walls with…
A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are…
We discuss the connection between the smooth and metric structure on quotient spaces, prove smoothness of isometries in special cases and discuss an application to a conjecture of Molino.
We investigate the invariant metrics and complex geodesics in the universal Teichm\"{u}ller space and Teichm\"{u}ller space of the punctured disk using Milin's coefficient inequalities. This technique allows us to establish that all…
It is widely accepted that Titan and the mid-sized regular satellites around Saturn were formed in the circum-Saturn disk. Thus, if these mid-sized satellites were simply accreted by collisions of similar ice-rock satellitesimals in the…
Recently Bishop constructed the first example of a bounded-type transcendental entire function with a wandering domain using a new technique called quasiconfomal folding. It is easy to check that his method produces an entire function of…
Curt McMullen showed that every compact orbit for the action of the diagonal group on the space of lattices contains a well-rounded lattice. We extend this to all closed orbits.
We examine dynamical systems with the property that pseudo-orbits can be traced by small diameter sets with bounded cardinality. In particular, we show that mixing sofic subshifts and surjective dynamical systems with the specification…
It has been demonstrated that systems of tightly packed inner planets with giant exterior companions tend to have less regular orbital spacings than those without such companions. We investigate whether this observed increase in the gap…
Motivated by the large number of extrasolar planetary systems that are near mean motion resonances, this paper explores a related type of dynamical behavior known as "nodding". Here, the resonance angle of a planetary system executes…