Symmetric interval identification systems of order three

Previous Article
Asymptotic analysis of the equations of motion for viscoelastic oldroyd fluid
DCDS Home
This Issue
Next Article
The periodic-parabolic logistic equation on $\mathbb{R}^N$

February 2012, 32(2): 643-656. doi: 10.3934/dcds.2012.32.643

Symmetric interval identification systems of order three

Alexandra Skripchenko ^1,

1.	Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russian Federation

Received November 2010 Revised June 2011 Published September 2011

Abstract
Related Papers

In the present paper we study symmetric interval identification systems of order three. We prove that the Rauzy induction preserves symmetry: for any symmetric interval identification system of order 3 after finitely many iterations of the Rauzy induction we always obtain a symmetric system. We also provide an example of symmetric interval identification system of thin type.

Keywords: Interval identification systems, Rauzy induction, $\mathbb{R}$-tree..

Mathematics Subject Classification: Primary: 37E05, 37E25; Secondary: 57M9.

Citation: Alexandra Skripchenko. Symmetric interval identification systems of order three. Discrete and Continuous Dynamical Systems, 2012, 32 (2) : 643-656. doi: 10.3934/dcds.2012.32.643

References:

[1]	M. Bestvina and M. Feighn, Stable actions of groups on real trees, Invent. Math., 121 (1995), 287-321.
[2]	M. Bestvina, $\mathbb{R}$-trees in topology, geometry, and group theory, in "Handbook of Geometric Topology," North-Holland, Amsterdam, (2002), 55-91.
[3]	M. Boshernitzan and I. Kornfeld, Interval translation mappings, Ergodic Theory and Dynamical Systems, 15 (1995), 821-832. doi: 10.1017/S0143385700009652.
[4]	H. Bruin and S. Troubetzkoy, The Gauss Map on a class of interval translation mappings, Israel J. Math, 137 (2003), 125-148. doi: 10.1007/BF02785958.
[5]	I. Dynnikov, Interval identification systems and plane sections of 3-periodic surfaces, Proceedings of the Steklov Institute of Mathematics, 263 (2008), 65-77. doi: 10.1134/S0081543808040068.
[6]	I. Dynnikov and B. Wiest, On the complexity of braids, J. Eur. Math. Soc., 9 (2007), 801-840. doi: 10.4171/JEMS/98.
[7]	I. Dynnikov, Semiclassical motion of the electron. A proof of the Novikov conjecture in general position and counterexamples, in "Solitons, Geometry, and Topology: On the Crossroad" AMS Transl., Ser. 2, 179, Amer. Math. Soc., Providence, RI, (1997), 45-73.
[8]	D. Gaboriau, Dynamique des systèmes d'isométries: Sur les bouts des orbits, Invent. Math., 126 (1996), 297-318. doi: 10.1007/s002220050101.
[9]	G. Levitt, La dynamique des pseudogroupes de rotations, Invent. Math., 113 (1993), 633-670. doi: 10.1007/BF01244321.
[10]	S. P. Novikov, The Hamiltonian formalism and many-valued analogue of Morse theory, Usp. Mat. Nauk, 37 (1982), 3-49.

show all references

References:

[1]	M. Bestvina and M. Feighn, Stable actions of groups on real trees, Invent. Math., 121 (1995), 287-321.
[2]	M. Bestvina, $\mathbb{R}$-trees in topology, geometry, and group theory, in "Handbook of Geometric Topology," North-Holland, Amsterdam, (2002), 55-91.
[3]	M. Boshernitzan and I. Kornfeld, Interval translation mappings, Ergodic Theory and Dynamical Systems, 15 (1995), 821-832. doi: 10.1017/S0143385700009652.
[4]	H. Bruin and S. Troubetzkoy, The Gauss Map on a class of interval translation mappings, Israel J. Math, 137 (2003), 125-148. doi: 10.1007/BF02785958.
[5]	I. Dynnikov, Interval identification systems and plane sections of 3-periodic surfaces, Proceedings of the Steklov Institute of Mathematics, 263 (2008), 65-77. doi: 10.1134/S0081543808040068.
[6]	I. Dynnikov and B. Wiest, On the complexity of braids, J. Eur. Math. Soc., 9 (2007), 801-840. doi: 10.4171/JEMS/98.
[7]	I. Dynnikov, Semiclassical motion of the electron. A proof of the Novikov conjecture in general position and counterexamples, in "Solitons, Geometry, and Topology: On the Crossroad" AMS Transl., Ser. 2, 179, Amer. Math. Soc., Providence, RI, (1997), 45-73.
[8]	D. Gaboriau, Dynamique des systèmes d'isométries: Sur les bouts des orbits, Invent. Math., 126 (1996), 297-318. doi: 10.1007/s002220050101.
[9]	G. Levitt, La dynamique des pseudogroupes de rotations, Invent. Math., 113 (1993), 633-670. doi: 10.1007/BF01244321.
[10]	S. P. Novikov, The Hamiltonian formalism and many-valued analogue of Morse theory, Usp. Mat. Nauk, 37 (1982), 3-49.

[1]	Sébastien Labbé. Rauzy induction of polygon partitions and toral $ \mathbb{Z}^2 $-rotations. Journal of Modern Dynamics, 2021, 17: 481-528. doi: 10.3934/jmd.2021017
[2]	Tayel Dabbous. Identification for systems governed by nonlinear interval differential equations. Journal of Industrial and Management Optimization, 2012, 8 (3) : 765-780. doi: 10.3934/jimo.2012.8.765
[3]	Marcelo F. Furtado, Liliane A. Maia, Elves A. B. Silva. Systems with coupling in $mathbb(R)^N$ class of noncoercive potentials. Conference Publications, 2003, 2003 (Special) : 295-304. doi: 10.3934/proc.2003.2003.295
[4]	Victoria Sadovskaya. Cohomology of $GL(2,\mathbb{R})$-valued cocycles over hyperbolic systems. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2085-2104. doi: 10.3934/dcds.2013.33.2085
[5]	Yuxia Guo, Bo Li. Nonexistence of positive solutions for polyharmonic systems in $\mathbb{R}^N_+$. Communications on Pure and Applied Analysis, 2016, 15 (3) : 701-713. doi: 10.3934/cpaa.2016.15.701
[6]	Armengol Gasull, Héctor Giacomini, Maite Grau. On the stability of periodic orbits for differential systems in $\mathbb{R}^n$. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 495-509. doi: 10.3934/dcdsb.2008.10.495
[7]	Marcello Lucia, Guido Sweers. Nondegeneracy of solutions for a class of cooperative systems on $ \mathbb{R}^n $. Communications on Pure and Applied Analysis, 2021, 20 (12) : 4177-4193. doi: 10.3934/cpaa.2021152
[8]	Edcarlos D. Silva, José Carlos de Albuquerque, Uberlandio Severo. On a class of linearly coupled systems on $ \mathbb{R}^N $ involving asymptotically linear terms. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3089-3101. doi: 10.3934/cpaa.2019138
[9]	Dongsheng Kang, Fen Yang. Semilinear elliptic systems involving multiple critical exponents and singularities in $\mathbb{R}^N$. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4247-4263. doi: 10.3934/dcds.2012.32.4247
[10]	Sachiko Ishida, Yusuke Maeda, Tomomi Yokota. Gradient estimate for solutions to quasilinear non-degenerate Keller-Segel systems on $\mathbb{R}^N$. Discrete and Continuous Dynamical Systems - B, 2013, 18 (10) : 2537-2568. doi: 10.3934/dcdsb.2013.18.2537
[11]	Megan Griffin-Pickering, Mikaela Iacobelli. Global strong solutions in $ {\mathbb{R}}^3 $ for ionic Vlasov-Poisson systems. Kinetic and Related Models, 2021, 14 (4) : 571-597. doi: 10.3934/krm.2021016
[12]	Xin Yang, Bing-Yu Zhang. Local well-posedness of the coupled KdV-KdV systems on $ \mathbb{R} $. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022002
[13]	Lun Guo, Wentao Huang, Huifang Jia. Ground state solutions for the fractional Schrödinger-Poisson systems involving critical growth in $ \mathbb{R} ^{3} $. Communications on Pure and Applied Analysis, 2019, 18 (4) : 1663-1693. doi: 10.3934/cpaa.2019079
[14]	Hooton Edward, Balanov Zalman, Krawcewicz Wieslaw, Rachinskii Dmitrii. Sliding Hopf bifurcation in interval systems. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3545-3566. doi: 10.3934/dcds.2017152
[15]	Jin-Mun Jeong, Seong-Ho Cho. Identification problems of retarded differential systems in Hilbert spaces. Evolution Equations and Control Theory, 2017, 6 (1) : 77-91. doi: 10.3934/eect.2017005
[16]	Giuseppina Barletta, Gabriele Bonanno. Multiplicity results to elliptic problems in $\mathbb{R}^N$. Discrete and Continuous Dynamical Systems - S, 2012, 5 (4) : 715-727. doi: 10.3934/dcdss.2012.5.715
[17]	Fernando Jiménez, Jürgen Scheurle. On the discretization of nonholonomic dynamics in $\mathbb{R}^n$. Journal of Geometric Mechanics, 2015, 7 (1) : 43-80. doi: 10.3934/jgm.2015.7.43
[18]	J. L. Barbosa, L. Birbrair, M. do Carmo, A. Fernandes. Globally subanalytic CMC surfaces in $\mathbb{R}^3$. Electronic Research Announcements, 2014, 21: 186-192. doi: 10.3934/era.2014.21.186
[19]	Thierry Cazenave, Flávio Dickstein, Fred B. Weissler. Universal solutions of the heat equation on $\mathbb R^N$. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1105-1132. doi: 10.3934/dcds.2003.9.1105
[20]	Giacomo Bocerani, Dimitri Mugnai. A fractional eigenvalue problem in $\mathbb{R}^N$. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 619-629. doi: 10.3934/dcdss.2016016

2021 Impact Factor: 1.588

Tools

Metrics

Other articles
by authors

on AIMS
Alexandra Skripchenko
on Google Scholar
Alexandra Skripchenko

[Back to Top]