Consider the geodesic flow on a real-analytic closed hypersurface \begin{document}$ M $\end{document} of id="M2">\begin{document}$ \mathbb{R}^n $\end{document}, equipped with induced metric. How commonly can we expect such flows to have transverse homoclinic orbit? In this pape...

Theorem 1.1 originates from the excess estimate of Abresch-Gromoll(c.f. Proposition 2.3 of [1]). The main ingredient of the proof is an application of maximum principle for subharmonic functions, and the existence of a poled function L such that ∆L ≥ 1. In our case, both maximum principle (Proposition 2.28 of [16]) and the existence of L(Lemma 2.36 of [16]) are known. For the convenience of rea...

Let G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent sequence of probability measures on G/Γ which are invariant and ergodic under actions of unipotent one-parameter subgroups, then the limit μ of such a sequence is supported on a closed orbit of the subgroup preserving it, and is invariant and ergodic for the action of a unipotent one-parameter subgroup of G.

There are dierent ways to code the geodesic flows on surfaces with negative curvature. Such code spaces give a useful tool to verify the dynamical properties of geodesic flows. Here we consider special subspaces of geodesic flows on Hecke surface whose arithmetic codings varies on a set with innite alphabet. Then we will compare the topological complexity of them by computing their topological ...

In this note we consider boundary perturbations in the A-Series unitary minimal models by φr,r+2 fields on superpositions of boundaries. In particular, we consider perturbations by boundary condition changing operators. Within conformal perturbation theory we explicitly map out the space of perturbative renormalisation group flows for the example φ13 and find that this sheds light on more gener...

Cocycles of Zm-actions on compact metric spaces provide a means for constructing Rm-actions or flows, called suspension flows. It is known that all Rm flows with a free dense orbit have an almost one-to-one extension which is a suspension flow. In this paper we investigate when the space for a suspension flow depends only on the given Zm-action and not on the actual cocycle. The identity map I ...