January 2014
Electronic Research Announcements in Mathematical Sciences;2014, Vol. 21, p89
Academic Journal
We study dynamical properties of direction foliations on the complex plane pulled back from direction foliations on a half-translation torus T, i.e., a torus equipped with a strict and integrable quadratic differential. If the torus T admits a pseudo-Anosov map we give a homological criterion for the appearance of dense leaves and leaves with bounded deviation on the universal covering of T, called Panov plane. Our result generalizes Dmitri Panov's explicit construction of dense leaves for certain arithmetic half-translation tori [33]. Certain Panov planes are related to the polygonal table of the periodic wind-tree model. In fact, we show that the dynamics on periodic wind-tree billiards can be converted to the dynamics on a pair of singular planes. Possible strategies to generalize our main dynamical result to larger sets of directions are discussed. Particularly we include recent results of Fraczek and Ulcigrai [17, 18] and Delecroix [6] for the wind-tree model. Implicitly Panov planes appear in Fraczek and Schmoll [15], where the authors consider Eaton Lens distributions.


Related Articles

  • Super (a, d)-H-Antimagic Covering on Tree Related Graphs. Roswitha, Mania; Utomo, Putranto Hadi; Martini, Titin Sri; Sari, Frety Kurnita; Kusmayadi, Tri Atmojo // AIP Conference Proceedings;2015, Vol. 1677 Issue 1, p030016-1 

    A simple graph G = (V(G), E(G)) admits an H-covering, if every edge belongs to subgraphs G isomorphic to H. An (a, d)-H-antimagic covering of G is a bijective function ξ V(G) ∪ E(G) → {1,2,…, ∣V(G)∣ + ∣V(G)∣}. For all subgraphs H' isomorphic to H, the H'...

  • Laminations and groups of homeomorphisms of the circle. Calegari, Danny; Dunfield, Nathan M. // Inventiones Mathematicae;Apr2003, Vol. 152 Issue 1, p149 

    If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that p1(M) acts on a circle. Here, we show that some other classes of essential laminations also give rise to actions on circles. In particular, we show this for tight essential laminations with solid torus guts. We also show...

  • Impact and compensation of I/Q imbalance on channel reciprocity of time-division-duplexing multiple-input multiple-output systems. Zu-Jun Liu; De-Chun Sun; Jie-Ling Wang; Ke-Chu Yi // IET Communications;2013, Vol. 7 Issue 7, p663 

    Direct-conversion-based wireless communication systems suffer from I/Q imbalances in the front-end analog processing. In this study, the authors investigate the impact of frequency-independent (FI) I/Q imbalance on the channel reciprocity of time-division-duplexing (TDD) multiple-input...

  • Combination of step sizes for affine projection algorithm with variable mixing parameter. Jong Hyun Choi; Hyeonwoo Cho; Jae Jin Jeong; Sang Woo Kim // Electronics Letters;8/29/2013, Vol. 49 Issue 18, p1 

    An algorithm that introduces a novel scheme for the combination of the two adaptation terms of the affine projection algorithm with different step sizes is proposed. The mixing parameter of the proposed algorithm is determined by minimising the mean-square deviation. The simulation results show...

  • Concerning an Analytical Solution of Some Families of Nonlinear Functional Equations. Perovich, S. M.; Bauk, S. I.; Jovanovic, M. Dj. // AIP Conference Proceedings;9/6/2007, Vol. 936 Issue 1, p412 

    The problem of finding the exact analytical closed-form solution of some families of non-linear functional equations is studied, in some detail, by the Special Trans Function Theory (STFT). The mathematical genesis of the analytical closed-form solutions and the structure of theoretical...

  • Numerical Solution for Laplace Equation with Mixed Boundary Condition for Ship Problem in the Sea. Silalahi, Fitriani Tupa R.; Budhi, Wono Setya; Adytia, Didit; van Groesen, E. // AIP Conference Proceedings;2015, Vol. 1677 Issue 1, p030006-1 

    One interesting phenomena is investigating the movement of ships at the sea. To start with the investigation in modelling of this problem, we will assume that the ship is only a one-dimensional object that is floating on the sea surface. Similarly, we assume that the water flow is uniform in...

  • The Properties of Q-Deformed Hyperbolic and Trigonometric Functions in Quantum Deformation. Deta, U. A.; Suparmi // AIP Conference Proceedings;2015, Vol. 1677 Issue 1, p030007-1 

    Quantum deformation has been studied due to its relation with applications in nuclear physics, conformal field theory, and statistical-quantum theory. The q-deformation of hyperbolic function was introduced by Arai. The application of q-deformed functions has been widely used in quantum...

  • Hawking Mass on Two Dimensional Surfaces. Radjabaycolle, Flinn C.; Akbar, Fiki T.; Gunara, Bobby E. // AIP Conference Proceedings;2015, Vol. 1677 Issue 1, p030010-1 

    In this paper, we study several aspects of the Hawking mass on two-dimensional surfaces defined as [1] m(Σ )=√∣Σ ∣/16π(1-1/16π∫Σ H2dσ-1/12π∫Σ R(ñ ñ) dσ) (1) where H, ñ and R are the mean curvature of the surface Σ, unit normal...

  • A Dynamical Model on Deposit and Loan of Banking: A Bifurcation Analysis. Sumarti, Novriana; Hasmi, Abrari Noor // AIP Conference Proceedings;2015, Vol. 1677 Issue 1, p030014-1 

    A dynamical model, which is one of sophisticated techniques using mathematical equations, can determine the observed state, for example bank profits, for all future times based on the current state. It will also show small changes in the state of the system create either small or big changes in...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics