thesis.bib

@article{mostovoy2004,
  author       = {Jacob Mostovoy},
  title        = {Lattices in $\mathbb{C}$ and Finite Subsets of a Circle},
  journaltitle = {The American Mathematical Monthly},
  publisher    = {Mathematical Association of America},
  year         = {2004},
  month        = {August},
  volume       = 111,
  number       = 4,
  pages        = {357--360}
}

@book{kassel2008,
    AUTHOR = {Kassel, Christian and Turaev, Vladimir},
     TITLE = {Braid groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {247},
      NOTE = {With the graphical assistance of Olivier Dodane},
 PUBLISHER = {Springer, New York},
      YEAR = {2008},
     PAGES = {xii+340},
      ISBN = {978-0-387-33841-5},
   MRCLASS = {20F36 (20C08 20F10 20F60 20M05 55R80 57M25 57M50)},
  MRNUMBER = {2435235},
MRREVIEWER = {Stephen P. Humphries},
       URL = {https://doi.org/10.1007/978-0-387-68548-9},
}

@incollection{ghys2007,
  author = {Ghys, \'{E}tienne},
     TITLE = {Knots and dynamics},
 BOOKTITLE = {International {C}ongress of {M}athematicians. {V}ol. {I}},
     PAGES = {247--277},
 PUBLISHER = {Eur. Math. Soc., Z\"urich},
      YEAR = {2007},
   MRCLASS = {37-02 (37C27 37D40 37E99 37J05 53D35 57M25)},
  MRNUMBER = {2334193},
MRREVIEWER = {Michael J. Usher},
       URL = {https://doi.org/10.4171/022-1/11},
}

@article{rademacher1956,
  author       = {Hans Rademacher},
  title        = {Zer Theorie der Dedekindschen Summen},
  journaltitle = {Mathematische Zeitschrift },
  year         = {1956},
  volume       = {63},
  pages        = {445-463}
}

@book{rademacher1972,
  author       = {Rademacher, Hans and Grosswald, Emil},
  title        = {Dedekind Sums},
  series       = {Carus Mathematical Monographs},
  publisher    = {Mathematical Association of America},
  location     = {Washington},
  year         = {1972}
}

@article{atiyah1987,
  author = {Atiyah, Michael},
  year = {1987},
  month = {03},
  pages = {335-380},
  title = {The logarithm of the dedekind $\eta$-function},
  volume = {278},
  journaltitle = {Mathematische Annalen}
}

@online{touristguide,
  author       = {Leys, Jos and Ghys, \'{E}tienne},
  title        = {Lorenz and modular flows: a visual introduction},
  subtitle     = {A tangled tale linking lattices, knots, templates, and strange attractors.},
  url          = {http://www.josleys.com/articles/ams_article/Lorenz3.htm},
  urldate      = {2017-11-06}
}

@article{ghys1991,
  author = {Barge, J and Ghys, E},
  year = {1992},
  month = {01},
  pages = {235-265},
  title = {Cocycles d'Euler et de Maslov},
  volume = {294},
  journaltitle = {Mathematische Annalen}
}

@book{hatcher2002,
  AUTHOR = {Hatcher, Allen},
   TITLE = {Algebraic topology},
PUBLISHER = {Cambridge University Press, Cambridge},
    YEAR = {2002},
   PAGES = {xii+544},
    ISBN = {0-521-79160-X; 0-521-79540-0},
 MRCLASS = {55-01 (55-00)},
MRNUMBER = {1867354},
MRREVIEWER = {Donald W. Kahn},
}

@book{stillwell1993,
    AUTHOR = {Stillwell, John},
     TITLE = {Classical topology and combinatorial group theory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {72},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1993},
     PAGES = {xii+334},
      ISBN = {0-387-97970-0},
   MRCLASS = {57M07 (20F99 57-01 57M50)},
  MRNUMBER = {1211642},
MRREVIEWER = {Bruno P. Zimmermann},
       URL = {https://doi.org/10.1007/978-1-4612-4372-4},
}

@book{knuth1992,
  title = {Literate Programming},
  author = {Knuth, Donald E.},
  publisher = {CSLI},
  year = {1994},
  location = {Stanford, California},
}

@misc{krainin1990,
  title =   {Memory \& Imagination: New Pathways to the Library of Congress},
  author = {Krainin, Julian and Lawrence, Michael R.},
  year = {1990},
}

@article{birman2012,
  title = {Lorenz knots},
  author = {Birman, Joan S.},
  year = {2012},
  url = {https://arxiv.org/abs/1201.0214v1},
}

@article{lorenz1963,
  title = {Deterministic Nonperiodic Flow}
}

@book{serre1973,
    AUTHOR = {Serre, Jean-Pierre},
     TITLE = {A Course in Arithmetic},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {7},
 PUBLISHER = {Springer, New York},
      YEAR = {1973},
      ISBN = {978-0-387-90040-7},
}

@book{abramowitz1964,
  title={Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables},
  author={Abramowitz, M. and Stegun, I.A.},
  isbn={9780486612720},
  lccn={lc65012253},
  series={Applied mathematics series},
  year={1964},
  publisher={Dover Publications}
}

@article{guckenheimer1979,
  AUTHOR = {Guckenheimer, John and Williams, R. F.},
  TITLE = {Structural stability of {L}orenz attractors},
  JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications
              Math\'ematiques},
  NUMBER = {50},
  YEAR = {1979},
  PAGES = {59--72},
  ISSN = {0073-8301},
  MRCLASS = {58F13 (58F25)},
  MRNUMBER = {556582},
  MRREVIEWER = {Zbigniew Nitecki},
  URL = {http://www.numdam.org/item?id=PMIHES_1979__50__59_0},
}

@inbook{guckenheimer1976,
  author="Guckenheimer, John",
  title="A Strange, Strange Attractor",
  bookTitle="The Hopf Bifurcation and Its Applications",
  year="1976",
  publisher="Springer New York",
  address="New York, NY",
  pages="368--381",
  abstract="Examples have been given by Abraham-Smale [1], Shub [1], and Newhouse [2] of diffeomorphisms on a compact manifold which are not in the closure of diffeomorphisms satisfying Smale's Axiom A or in the closure of the set of $\Omega$-stable diffeomorphisms (Smale [1]). The suspension construction (Smale [1]) allows one to give analogous examples for vector fields on compact manifolds.",
  isbn="978-1-4612-6374-6",
  doi="10.1007/978-1-4612-6374-6_25",
  url="https://doi.org/10.1007/978-1-4612-6374-6_25"
}

@book{milnor1968,
  title={Singular Points of Complex Hypersurfaces},
  author={Milnor, J.W.},
  isbn={9780691080659},
  lccn={lc69017408},
  series={Annals of mathematics studies},
  url={https://books.google.com/books?id=cuAAFbBYlSsC},
  year={1968},
  publisher={Princeton University Press}
}

@online{graphicallinearalgebra,
  author       = {Pawel Sobocinski, Filippo Bonchi, Fabio Zanasi},
  title        = {Graphical Linear Algebra},
  url          = {https://graphicallinearalgebra.net/},
  urldate      = {2018-03-23}
}

@article{arnold66,
    AUTHOR = {Arnold, V.},
     TITLE = {Sur la g\'eom\'etrie diff\'erentielle des groupes de {L}ie de
              dimension infinie et ses applications \`a l'hydrodynamique des
              fluides parfaits},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {16},
      YEAR = {1966},
    NUMBER = {fasc. 1},
     PAGES = {319--361},
      ISSN = {0373-0956},
   MRCLASS = {57.50 (57.55)},
  MRNUMBER = {0202082},
MRREVIEWER = {R. Hermann},
       URL = {http://www.numdam.org/item?id=AIF_1966__16_1_319_0},
}

@online{tao,
  author       = {Terence Tao},
  title        = {The Euler-Arnold equation},
  url          = {https://terrytao.wordpress.com/2010/06/07/the-euler-arnold-equation},
  date = {2010-06-07},
  urldate      = {2018-04-17}
}

@book{katok1992,
  title={Fuchsian Groups},
  author={Katok, S.},
  isbn={9780226425825},
  lccn={lc92006535},
  series={Chicago Lectures in Mathematics},
  url={https://books.google.com/books?id=pJ2Se3tCr-cC},
  year={1992},
  publisher={University of Chicago Press}
}

@book{silverman1994,
  title={Advanced Topics in the Arithmetic of Elliptic Curves},
  author={Silverman, J.H.},
  isbn={9780387943251},
  lccn={94021787},
  series={Graduate texts in mathematics},
  url={https://books.google.com/books?id=dnZ0Vdo-7BsC},
  year={1994},
  publisher={Springer-Verlag}
}

@online{ncatcafe,
  author       = {Bartlett, Bruce and Willerton, Simon},
  title        = {The Modular Flow on the Space of Lattices},
  date      = {2014-04-07},
  urldate = {2018-04-20},
  url = {https://golem.ph.utexas.edu/category/2014/04/the_modular_flow_on_the_space.html}
}

@book{rankin1977modular,
  title={Modular forms and functions},
  author={Rankin, Robert A},
  year={1977},
  publisher={Cambridge University Press}
}