American Institute of Mathematical Sciences

Advanced
August  2010, 27(3): 863-906. doi: 10.3934/dcds.2010.27.863

Decoration invariants for horseshoe braids

André de Carvalho 1, and  Toby Hall 2,

1. 

Departamento de Matemática Aplicada, IME-USP, Rua Do Matão 1010, Cidade Universitária, 05508-090 São Paulo SP, Brazil
2. 

Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom

Received  June 2009 Revised  September 2009 Published  March 2010

The Decoration Conjecture describes the structure of the set of braid types of Smale's horseshoe map ordered by forcing, providing information about the order in which periodic orbits can appear when a horseshoe is created. A proof of this conjecture is given for the class of so-called lone decorations, and it is explained how to calculate associated braid conjugacy invariants which provide additional information about forcing for horseshoe braids.
Keywords: Forcing relations, Horseshoe, Decoration conjecture..
Mathematics Subject Classification: Primary: 37E30, 37E15, 37B10, 37B4.
Citation: André de Carvalho, Toby Hall. Decoration invariants for horseshoe braids. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 863-906. doi: 10.3934/dcds.2010.27.863
[1]

Marcus Fontaine, William D. Kalies, Vincent Naudot. A reinjected cuspidal horseshoe. Conference Publications, 2013, 2013 (special) : 227-236. doi: 10.3934/proc.2013.2013.227
[2]

Christian Bonatti, Stanislav Minkov, Alexey Okunev, Ivan Shilin. Anosov diffeomorphism with a horseshoe that attracts almost any point. Discrete & Continuous Dynamical Systems - A, 2020, 40 (1) : 441-465. doi: 10.3934/dcds.2020017
[3]

Stephen Doty and Anthony Giaquinto. Generators and relations for Schur algebras. Electronic Research Announcements, 2001, 7: 54-62.

[4]

Christophe Cheverry, Adrien Fontaine. Dispersion relations in cold magnetized plasmas. Kinetic & Related Models, 2017, 10 (2) : 373-421. doi: 10.3934/krm.2017015
[5]

Artur Babiarz, Adam Czornik, Michał Niezabitowski, Evgenij Barabanov, Aliaksei Vaidzelevich, Alexander Konyukh. Relations between Bohl and general exponents. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5319-5335. doi: 10.3934/dcds.2017231
[6]

Evelyn Sander. Hyperbolic sets for noninvertible maps and relations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 339-357. doi: 10.3934/dcds.1999.5.339
[7]

Roman Shvydkoy, Eitan Tadmor. Eulerian dynamics with a commutator forcing Ⅱ: Flocking. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5503-5520. doi: 10.3934/dcds.2017239
[8]

Alex Eskin, Gregory Margulis and Shahar Mozes. On a quantitative version of the Oppenheim conjecture. Electronic Research Announcements, 1995, 1: 124-130.

[9]

Uri Shapira. On a generalization of Littlewood's conjecture. Journal of Modern Dynamics, 2009, 3 (3) : 457-477. doi: 10.3934/jmd.2009.3.457
[10]

Michael Hutchings, Frank Morgan, Manuel Ritore and Antonio Ros. Proof of the double bubble conjecture. Electronic Research Announcements, 2000, 6: 45-49.

[11]

G. A. Swarup. On the cut point conjecture. Electronic Research Announcements, 1996, 2: 98-100.

[12]

Janos Kollar. The Nash conjecture for threefolds. Electronic Research Announcements, 1998, 4: 63-73.

[13]

Roman Shvydkoy. Lectures on the Onsager conjecture. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : 473-496. doi: 10.3934/dcdss.2010.3.473
[14]

Joel Hass, Michael Hutchings and Roger Schlafly. The double bubble conjecture. Electronic Research Announcements, 1995, 1: 98-102.

[15]

Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann. On the torsion in the center conjecture. Electronic Research Announcements, 2018, 25: 27-35. doi: 10.3934/era.2018.25.004
[16]

Ziteng Wang, Shu-Cherng Fang, Wenxun Xing. On constraint qualifications: Motivation, design and inter-relations. Journal of Industrial & Management Optimization, 2013, 9 (4) : 983-1001. doi: 10.3934/jimo.2013.9.983
[17]

Luca Lussardi, Stefano Marini, Marco Veneroni. Stochastic homogenization of maximal monotone relations and applications. Networks & Heterogeneous Media, 2018, 13 (1) : 27-45. doi: 10.3934/nhm.2018002
[18]

Joshua Du, Liancheng Wang. Dispersion relations for supersonic multiple virtual jets. Conference Publications, 2011, 2011 (Special) : 381-390. doi: 10.3934/proc.2011.2011.381
[19]

Gerhard Frey. Relations between arithmetic geometry and public key cryptography. Advances in Mathematics of Communications, 2010, 4 (2) : 281-305. doi: 10.3934/amc.2010.4.281
[20]

Yves Bourgault, Damien Broizat, Pierre-Emmanuel Jabin. Convergence rate for the method of moments with linear closure relations. Kinetic & Related Models, 2015, 8 (1) : 1-27. doi: 10.3934/krm.2015.8.1

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (21)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences