Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

The Use Of Social Media And Collaborative Tools For Virtual Teaming - A Global Market Reach Out By Navibank

In recent years, social networking sites have witnessed a signi?cant growth in popularity and membership. These social networking sites like Facebook or LinkedIn use tools that also appeal to businesses. One important area of business application of social networking is to improve communication and trust relationships among virtual project teams (Sarker, Ahuja & Kirkeby, 2011; Anantatmula & Thomas, 2010). In this paper, the authors report the use of social media tools for virtual teaming for a large Vietnamese bank, Navibank.  The paper delves into the strategic initiative and expansion into global markets using virtual project teams that communicated mostly through social media tools and services.  Navibank (hereafter known as the Bank) is one of the top ten largest commercial banks in Vietnam. In a large project of opening ten branches of the Bank in Cambodia by the end of 2015, social media tools like Skype, e-mail, Facebook, instant messaging and video conference are being used by the Bank teams in Vietnam to communicate and work effectively with the new teams that are being formed in Cambodia

Entire holomorphic curves into projective spaces intersecting a generic hypersurface of high degree

In this note, we establish the following Second Main Theorem type estimate for every entire non-algebraically degenerate holomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{P}^n(\mathbb{C})$, in present of a {\slgeneric} hypersuface $D\subset\mathbb{P}^n(\mathbb{C})$ of sufficiently high degree $d\geq 15(5n+1)n^n$: $$T_f(r) \leq \,N_f^{[1]}(r,D) + O\big(\log T_f(r) + \log r \big)\parallel,$$ where $T_f(r)$ and $N_f^{[1]}(r,D)$ stand for the order function and the $1$-truncated counting function in Nevanlinna theory. This inequality quantifies recent results on the logarithmic Green-Griffiths conjecture