American Institute of Mathematical Sciences

Advanced
October  2009, 3(4): 589-594. doi: 10.3934/jmd.2009.3.589

Foliations with unbounded deviation on $\mathbb T^2$

Dmitri Panov 1,

1. 

Department of Mathematics, South Kensington Campus, Imperial College London, London, SW7 2AZ, United Kingdom

Received  July 2009 Revised  August 2009 Published  January 2010

We study $C^{\infty}$-foliations with $3$ singular points on $\mathbb T^2$ whose lift to $\mathbb R^2$ has connected leaves that are dense subsets of $\mathbb R^2$.
Keywords: pseudo-Anosov map, quadratic differential., Unstable foliation.
Mathematics Subject Classification: Primary: 37E35; Secondary: 57M5.
Citation: Dmitri Panov. Foliations with unbounded deviation on $\mathbb T^2$. Journal of Modern Dynamics, 2009, 3 (4) : 589-594. doi: 10.3934/jmd.2009.3.589
[1]

Chris Johnson, Martin Schmoll. Pseudo-Anosov eigenfoliations on Panov planes. Electronic Research Announcements, 2014, 21: 89-108. doi: 10.3934/era.2014.21.89
[2]

Kariane Calta, Thomas A. Schmidt. Infinitely many lattice surfaces with special pseudo-Anosov maps. Journal of Modern Dynamics, 2013, 7 (2) : 239-254. doi: 10.3934/jmd.2013.7.239
[3]

S. Öykü Yurttaş. Dynnikov and train track transition matrices of pseudo-Anosov braids. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 541-570. doi: 10.3934/dcds.2016.36.541
[4]

Hieu Trung Do, Thomas A. Schmidt. New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant. Journal of Modern Dynamics, 2016, 10: 541-561. doi: 10.3934/jmd.2016.10.541
[5]

Eric Bedford, Serge Cantat, Kyounghee Kim. Pseudo-automorphisms with no invariant foliation. Journal of Modern Dynamics, 2014, 8 (2) : 221-250. doi: 10.3934/jmd.2014.8.221
[6]

Juan Alonso, Nancy Guelman, Juliana Xavier. Actions of solvable Baumslag-Solitar groups on surfaces with (pseudo)-Anosov elements. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 1817-1827. doi: 10.3934/dcds.2015.35.1817
[7]

C. M. Groothedde, J. D. Mireles James. Parameterization method for unstable manifolds of delay differential equations. Journal of Computational Dynamics, 2017, 4 (1&2) : 21-70. doi: 10.3934/jcd.2017002
[8]

Tibor Krisztin. A local unstable manifold for differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 993-1028. doi: 10.3934/dcds.2003.9.993
[9]

Arne Ogrowsky, Björn Schmalfuss. Unstable invariant manifolds for a nonautonomous differential equation with nonautonomous unbounded delay. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1663-1681. doi: 10.3934/dcdsb.2013.18.1663
[10]

M. Jotz. The leaf space of a multiplicative foliation. Journal of Geometric Mechanics, 2012, 4 (3) : 313-332. doi: 10.3934/jgm.2012.4.313
[11]

Jaume Llibre, Claudia Valls. Algebraic limit cycles for quadratic polynomial differential systems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2475-2485. doi: 10.3934/dcdsb.2018070
[12]

Lanzhe Liu. Mean oscillation and boundedness of Toeplitz Type operators associated to pseudo-differential operators. Communications on Pure & Applied Analysis, 2015, 14 (2) : 627-636. doi: 10.3934/cpaa.2015.14.627
[13]

JIAO CHEN, WEI DAI, GUOZHEN LU. $L^p$ boundedness for maximal functions associated with multi-linear pseudo-differential operators. Communications on Pure & Applied Analysis, 2017, 16 (3) : 883-898. doi: 10.3934/cpaa.2017042
[14]

João P. Almeida, Albert M. Fisher, Alberto Adrego Pinto, David A. Rand. Anosov diffeomorphisms. Conference Publications, 2013, 2013 (special) : 837-845. doi: 10.3934/proc.2013.2013.837
[15]

Alain Bensoussan, Shaokuan Chen, Suresh P. Sethi. Linear quadratic differential games with mixed leadership: The open-loop solution. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 95-108. doi: 10.3934/naco.2013.3.95
[16]

Kai Du, Jianhui Huang, Zhen Wu. Linear quadratic mean-field-game of backward stochastic differential systems. Mathematical Control & Related Fields, 2018, 8 (3&4) : 653-678. doi: 10.3934/mcrf.2018028
[17]

Ildoo Kim. An $L_p$-Lipschitz theory for parabolic equations with time measurable pseudo-differential operators. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2751-2771. doi: 10.3934/cpaa.2018130
[18]

Jeffrey J. Early, Juha Pohjanpelto, Roger M. Samelson. Group foliation of equations in geophysical fluid dynamics. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1571-1586. doi: 10.3934/dcds.2010.27.1571
[19]

José Santana Campos Costa, Fernando Micena. Pathological center foliation with dimension greater than one. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 1049-1070. doi: 10.3934/dcds.2019044
[20]

Zhiyu Wang, Yan Guo, Zhiwu Lin, Pingwen Zhang. Unstable galaxy models. Kinetic & Related Models, 2013, 6 (4) : 701-714. doi: 10.3934/krm.2013.6.701

2018 Impact Factor: 0.295

Tools

Metrics

  • PDF downloads (15)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences