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%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Jair Koiller at 2019-05-25 16:00:32 -0300
%% Saved with string encoding Unicode (UTF-8)
@book{ArnoldAvez,
Author = {V. I Arnold AND A. Avez},
Date-Added = {2019-05-25 16:49:51 +0000},
Date-Modified = {2019-05-25 16:50:53 +0000},
Publisher = {Benjamin},
Title = {Ergodic Problems of Classical Mechanics},
Year = {1968}}
@article{Mineur,
Author = {Henry Mineur},
Date-Added = {2019-05-25 16:39:33 +0000},
Date-Modified = {2019-05-25 16:40:37 +0000},
Journal = {J. Math. Pures Appl.},
Pages = {385-389},
Title = {R{\'e}duction des syst{\`e}mes m{\'e}caniques {\`a} n degr{\'e}s de libert{\'e} admettant n int{\'e}grales premi{\`e}res uniformes en involution aux syst{\`e}mes {\`a} variables s{\'e}par{\'e}es},
Volume = {15},
Year = {1936}}
@article{Dullin:2016ft,
Abstract = {We give a complete symbolic dynamics description of the dynamics of Euler's problem of two fixed centers. By analogy with the 3-body problem we use the collinearities (or syzygies) of the three bodies as symbols. We show that motion without collision on regular tori of the regularised integrable system are given by so called Sturmian sequences. Sturmian sequences were introduced by Morse and Hedlund in 1940. Our main theorem is that the periodic Sturmian sequences are in one to one correspondence with the periodic orbits of the two center problem. Similarly, finite Sturmian sequences correspond to collision--collision orbits.},
Author = {Dullin, Holger R and Montgomery, Richard},
Booktitle = {Nonlinearity},
Da = {2016/03/09},
Date-Added = {2019-05-23 19:45:27 +0000},
Date-Modified = {2019-05-23 19:45:27 +0000},
Doi = {10.1088/0951-7715/29/4/1212},
Isbn = {0951-7715; 1361-6544},
Number = {4},
Pages = {1212-1237},
Publisher = {IOP Publishing},
Title = {Syzygies in the two center problem},
Ty = {JOUR},
Url = {http://dx.doi.org/10.1088/0951-7715/29/4/1212},
Volume = {29},
Year = {2016},
Bdsk-Url-1 = {http://dx.doi.org/10.1088/0951-7715/29/4/1212}}
@article{Birkhoff1927,
Author = {Birkhoff, George D.},
Da = {1927/12/01},
Date-Added = {2019-05-23 19:14:00 +0000},
Date-Modified = {2019-05-23 19:25:09 +0000},
Doi = {10.1007/BF02421325},
Id = {Birkhoff1927},
Isbn = {1871-2509},
Journal = {Acta Mathematica},
Number = {1},
Pages = {359--379},
Title = {On the periodic motions of dynamical systems},
Ty = {JOUR},
Url = {https://doi.org/10.1007/BF02421325},
Volume = {50},
Year = {1927},
Bdsk-Url-1 = {https://doi.org/10.1007/BF02421325}}
@book{Jacobivorlesungen,
Author = {C. G. J. Jacobi},
Date-Added = {2019-05-23 18:56:30 +0000},
Date-Modified = {2019-05-23 19:09:24 +0000},
Editor = {Alfred Clebsch},
Keywords = {http://sites.mathdoc.fr/cgi-bin/oeitem?id=OE_JACOBI__8_1_0},
Publisher = {G. Reimer},
Title = {Vorlesungen \"uber Dynamik gehalten an der Universit\"at zu K\"onigsberg im Wintersemester 1842-1843},
Year = {1866}}
@article{Euler,
Author = {Leonhard Euler},
Booktitle = {Opera Omnia},
Date-Added = {2019-05-23 18:37:18 +0000},
Date-Modified = {2019-05-23 18:42:28 +0000},
Journal = {Novi Commentarii academiae scientiarum Petropolitanae},
Pages = {207-242},
Title = {De motu corporis ad duo centra virium fixa attracti (Opera Omnia: Series 2, Volume 6, pp. 209 - 246, available online http://eulerarchive.maa.org/pages/E301.html)},
Year = {1766}}
@article{Jacobi2,
Author = {C. G. J. Jacobi},
Date-Added = {2019-05-23 18:16:03 +0000},
Date-Modified = {2019-05-23 18:25:26 +0000},
Journal = {Journal de math\'ematiques pures et appliqu\'ees 1re s\'erie},
Pages = {267-272},
Title = {De la ligne g\'eod\'esique sur un ellipso\"ide, et des diff\'erents usages d'une transformation analytique remarquable.},
Volume = {6},
Year = {1841}}
@article{Jacobi1,
Author = {C. G. J. Jacobi},
Date-Added = {2019-05-23 18:12:09 +0000},
Date-Modified = {2019-05-23 18:15:10 +0000},
Journal = {Journal f"ur die Reine und Angewandte Mathematik (Crelles Journal)},
Keywords = {doi:10.1515/crll.1839.19.309},
Pages = {309-313},
Title = {Note von der geod\"atischen Linie auf einem Ellipsoid und den verschiedenen Anwendungen einer merkw\"urdigen analytischen Substitution [The geodesic on an ellipsoid and various applications of a remarkable analytical substitution].},
Volume = {19},
Year = {1839}}
@article{Moser:1978xq,
Author = {Moser, J{\"u}rgen},
Da = {1978/06/01},
Date-Added = {2019-05-23 17:44:04 +0000},
Date-Modified = {2019-05-23 17:44:04 +0000},
Doi = {10.1007/BF03023062},
Id = {Moser1978},
Isbn = {0343-6993},
Journal = {The Mathematical Intelligencer},
Number = {2},
Pages = {65--71},
Title = {Is the solar system stable?},
Ty = {JOUR},
Url = {https://doi.org/10.1007/BF03023062},
Volume = {1},
Year = {1978},
Bdsk-Url-1 = {https://doi.org/10.1007/BF03023062}}
@book{Tabachnikov2005,
Author = {Tabachnikov, S. },
Date-Added = {2019-05-23 17:38:20 +0000},
Date-Modified = {2019-05-25 16:42:21 +0000},
Editor = {Pennsylvania State University. Mathematics Advanced Study Semesters},
Isbn = {9780821839195},
Publisher = {American Mathematical Society},
Title = {Geometry and Billiards},
Title1 = {Student mathematical library},
Ty = {BOOK},
Url = {https://books.google.com.br/books?id=QrDxBwAAQBAJ},
Year = {2005},
Bdsk-Url-1 = {https://books.google.com.br/books?id=QrDxBwAAQBAJ}}
@book{poncelet1864applications,
Author = {Poncelet, J.V.},
Date-Added = {2019-05-23 17:36:25 +0000},
Date-Modified = {2019-05-23 17:36:25 +0000},
Number = {pt. 2},
Publisher = {Gauthier-Villars},
Series = {Applications d'analyse et de g{\'e}om{\'e}trie: qui ont servi de principal fondement au trait{\'e} des propri{\'e}t{\'e}s projectives des figures},
Title = {Applications d'analyse et de g{\'e}om{\'e}trie: qui ont servi de principal fondement au trait{\'e} des propri{\'e}t{\'e}s projectives des figures},
Url = {https://books.google.com.br/books?id=BGUVAAAAQAAJ},
Year = {1864},
Bdsk-Url-1 = {https://books.google.com.br/books?id=BGUVAAAAQAAJ}}
@book{Dragovicbook,
Author = {Vladimir Dragovi\'c AND Milena Radnovi\'c},
Date-Added = {2019-05-23 15:27:41 +0000},
Date-Modified = {2019-05-23 15:29:19 +0000},
Publisher = {Springer, Basel},
Title = {Poncelet Porisms and Beyond Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics},
Year = {2011}}
@article{Chang:1988bf,
Annote = {doi: 10.1063/1.527900},
Author = {Chang,Shau-Jin and Friedberg,Richard},
Booktitle = {Journal of Mathematical Physics},
Da = {1988/07/01},
Date = {1988/07/01},
Date-Added = {2019-05-23 15:25:13 +0000},
Date-Modified = {2019-05-23 15:25:31 +0000},
Doi = {10.1063/1.527900},
Isbn = {0022-2488},
Journal = {Journal of Mathematical Physics},
Journal1 = {Journal of Mathematical Physics},
M3 = {doi: 10.1063/1.527900},
Month = {2019/05/23},
Number = {7},
Pages = {1537--1550},
Publisher = {American Institute of Physics},
Title = {Elliptical billiards and Poncelet's theorem},
Ty = {JOUR},
Url = {https://doi.org/10.1063/1.527900},
Volume = {29},
Year = {1988},
Year1 = {1988},
Bdsk-Url-1 = {https://doi.org/10.1063/1.527900}}
@book{Birkhoff,
Author = {G. D. Birkhoff},
Date-Added = {2019-05-23 15:18:40 +0000},
Date-Modified = {2019-05-23 15:20:01 +0000},
Editor = {American Mathematical Society Colloquium Publications},
Publisher = {American Mathematical Society, Providence, RI},
Title = {Dynamical Systems},
Year = {1966}}
@book{Crelle:1839rm,
Author = {Crelle, A. L. and Borchardt, C. W. and Kronecker, L. and Fuchs, L. and Hensel, K. W. S. and Hasse, H. and Schottky, F. H.},
Date-Added = {2019-05-23 15:17:41 +0000},
Date-Modified = {2019-05-23 15:17:41 +0000},
Number = {vol. 19},
Publisher = {W. de Gruyter},
Title = {Journal f{\"u}r die reine und angewandte Mathematik},
Ty = {BOOK},
Url = {https://books.google.com.br/books?id=RbwGAAAAYAAJ},
Year = {1839},
Bdsk-Url-1 = {https://books.google.com.br/books?id=RbwGAAAAYAAJ}}
@article{Jacobiporisms,
Author = {Jacob, C.G.J.},
Date-Added = {2019-05-23 15:16:21 +0000},
Date-Modified = {2019-05-23 15:16:42 +0000},
Journal = {J. Reine Angew. Math.},
Month = {05},
Pages = {376-387},
Title = {{\"U}ber die Anwendung der elliptischen Transcendentten auf ein bekanntes Problem der Elementargeometrie},
Volume = {3},
Year = {2019}}
@article{PINTO-DE-CARVALHO:2013fk,
Abstract = {A caustic of a billiard table is a curve such that any billiard trajectory, once tangent to the curve, stays tangent after every reflection at the boundary. When the billiard table is an ellipse, any non-singular billiard trajectory has a caustic, which can be either a confocal ellipse or a confocal hyperbola. Resonant caustics---those whose tangent trajectories are closed polygons---are destroyed under generic perturbations of the billiard table. We prove that none of the resonant elliptical caustics persists under a large class of explicit perturbations of the original ellipse. This result follows from a standard Melnikov argument and the analysis of the complex singularities of certain elliptic functions.},
Author = {PINTO-DE-CARVALHO, S{\^O}NIA and RAM{\'I}REZ-ROS, RAFAEL},
Booktitle = {Ergodic Theory and Dynamical Systems},
Date-Added = {2019-05-23 15:15:33 +0000},
Date-Modified = {2019-05-23 15:15:33 +0000},
Db = {Cambridge Core},
Doi = {DOI: 10.1017/S0143385712000417},
Dp = {Cambridge University Press},
Et = {2012/08/21},
Isbn = {0143-3857},
Number = {6},
Pages = {1876-1890},
Publisher = {Cambridge University Press},
Title = {Non-persistence of resonant caustics in perturbed elliptic billiards},
Ty = {JOUR},
Url = {https://www.cambridge.org/core/article/nonpersistence-of-resonant-caustics-in-perturbed-elliptic-billiards/252AB20915C3EAAEE3EF432FE64E7427},
Volume = {33},
Year = {2013},
Bdsk-Url-1 = {https://www.cambridge.org/core/article/nonpersistence-of-resonant-caustics-in-perturbed-elliptic-billiards/252AB20915C3EAAEE3EF432FE64E7427},
Bdsk-Url-2 = {https://doi.org/10.1017/S0143385712000417}}