116
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Pentagram Spirals

Pages 384-405 | Published online: 09 Dec 2013

XXX

  • Fock , [Fock and Marshakov 13] V. and Marshakov , A. 2013 . “ Integrable Systems, Clusters, Dimers and Loop Groups ” . Preprint
  • Gekhtman , [Gekhtman et al. 12] M. , Shapiro , M. , Tabachnikov , S. and Vainshtein , A. 2012 . Higher Pentagram Maps, Weighted Directed Networks, and Cluster Dynamics . Electron. Res. Announc. Math. Sci. , 19 : 1 – 17 .
  • Glick , [Glick 11] M. The Pentagram Map and Y -Patterns . 23rd Int. Conf. on Formal Power Series and Alg. Combinatorics (FPSAC 2011) , pp. 399 – 410 .
  • Glick , [Glick 12] M. 2012 . The Pentagram Map and Y -Patterns . Adv. Math. , 227 : 1019 – 1045 .
  • Goncharov , [Goncharov and Kenyon 11] A. B. and Kenyon , R. 2011 . “ Dimers and Cluster Integrable Systems ” . arXiv 1107.5588
  • Kedem , [Kedem and DiFrancesco 12] R. and DiFrancesco , P. 2012 . “ T -Systems with Boundaries from Network Solutions ” . arXiv 1208.4333
  • Khesin , [Khesin and Soloviev 13] B. and Soloviev , F. 2013 . Integrability of Higher Pentagram Maps . Mathem. Annalen , 357 ( 3 ) : 1005 – 1047 .
  • Marí Beffa , [Marí Beffa 13a] G. 2013 . “ On Generalizations of the Pentagram Map: Discretizations of AGD Flows ” . arXiv:1303.5047
  • Marí Beffa , [Marí Beffa 13b] G. 2013 . “ On Integrable Generalizations of the Pentagram Map ” . arXiv:1303.4295
  • Motzkin , [Motzkin 45] Th. 1945 . The Pentagon in the Projective Plane, with a Comment on Napieros Rule . Bull. Amer. Math. Soc. , 52 : 985 – 989 .
  • Ovsienko , [Ovsienko et al. 09] V. , Schwartz , R. and Tabachnikov , S. 2009 . Quasiperiodic Motion for the Pentagram Map . Electron. Res. Announc. Math. Sci. , 16 : 1 – 8 .
  • Ovsienko , [Ovsienko et al. 10] V. , Schwartz , R. and Tabachnikov , S. 2010 . The pentagram Map: A Discrete Integrable System . Comm. Math. Phys. , 299 : 409 – 446 .
  • Ovsienko , [Ovsienko et al. 13] V. , Schwartz , R. and Tabachnikov , S. 2013 . Liouville–Arnold Integrability of the Pentagram Map on Closed Polygons . Duke Math. J. , 162 : 12 – 2196 . 2149
  • Schwartz , [Schwartz 92] R. 1992 . The Pentagram Map . Experiment. Math. , 1 : 71 – 81 .
  • Schwartz , [Schwartz 01] R. 2001 . The Pentagram Map Is Recurrent . Experiment. Math. , 10 : 519 – 528 .
  • Schwartz , [Schwartz 06] R. 2006 . A Conformal Averaging Process on the Circle . Geom. Dedicata , 117 : 19 – 46 .
  • Schwartz , [Schwartz 08] R. 2008 . Discrete Monodromy, Pentagrams, and the Method of Condensation . J. of Fixed Point Theory and Appl. , 3 : 379 – 409 .
  • Schwartz , [Schwartz and Tabachnikov 10] R. and Tabachnikov , S. 2010 . Elementary Surprises in Projective Geometry . Math. Intelligencer , 32 : 31 – 34 .
  • Soloviev , [Soloviev 13] F. 2013 . Integrability of the Pentagram Map . Duke Math J. , To appear in

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.