@MISC{li2020lebesgue,
title="{Lebesgue Measure Preserving Thompson's Monoid}",
author={William Li},
year={2020},
journal = {arXiv e-prints},
month = {09},
pages ={arXiv:2010.00167},
howpublished={\url{https://arxiv.org/abs/2010.00167}},
NOTE = {arXiv e-prints, arXiv:2010.00167}
}
@ARTICLE{2019arXiv190607558B,
author = {{Bobok}, Jozef and {Troubetzkoy}, Serge},
title = "{Typical properties of interval maps preserving the Lebesgue measure}",
journal = {Nonlinearity},
year = {2020},
month = {10},
volume = {33},
number = {12},
pages = {6461--6479},
}
@ARTICLE{1996CFP,
author = {{Cannon}, J.W. and {Floyd}, W.J. and {Parry}, W.R.},
title = "{Introductory notes on Richard Thompson's groups}",
journal = {Enseign. Math.},
year = 1996,
volume = 42,
pages = {215-256},
}
% journal = {Enseignement Math\'ematique},
@article{2016Akin,
author = {Akin, Ethan and Auslander, Joseph and Nagar, Anima},
year = {2016},
month = {02},
pages = {},
title = {Variations on the Concept of Topological Transitivity},
volume = {235},
journal = {Studia Math.},
doi = {10.4064/sm8553-7-2016}
}
%journal = {Studia Mathematica},
@ARTICLE{ruette2015chaos,
title={Chaos on the interval - a survey of relationship between the various kinds of chaos for continuous interval maps},
author={Sylvie Ruette},
journal = {arXiv e-prints},
year={2015},
month = {04},
eprint={1504.03001},
pages = {arXiv:1504.03001},
}
@book{ruette2017chaos,
title={Chaos on the Interval},
author={Ruette, S.},
isbn={9781470429560},
lccn={2016042280},
series={University Lecture Series},
url={https://books.google.com/books?id=IkBIDgAAQBAJ},
year={2017},
publisher={American Mathematical Society}
}
@article{10.2307/44153684,
ISSN = {01471937, 19301219},
URL = {http://www.jstor.org/stable/44153684},
author = {J. Bobok},
journal = {Real Anal. Exch.},
number = {1},
pages = {119--129},
publisher = {Michigan State University Press},
title = {On non-differentiable measure-preserving functions},
volume = {16},
year = {1990}
}
% journal = {Real Analysis Exchange},
@inproceedings{10.1007/11496137_11,
author = {Shpilrain, Vladimir and Ushakov, Alexander},
title = {Thompson’s Group and Public Key Cryptography},
year = {2005},
isbn = {3540262237},
publisher = {Springer-Verlag},
address = {Berlin, Heidelberg},
url = {https://doi.org/10.1007/11496137_11},
doi = {10.1007/11496137_11},
booktitle = {Applied Cryptography and Network Security},
pages = {151–163},
numpages = {13},
location = {New York, NY},
series = {ACNS’05}
}
%booktitle = {Proceedings of the Third International Conference on Applied Cryptography and Network Security},
@MISC{notesonperronfrobenius,
title = {PERRON {F}ROBENIUS {T}HEOREM},
author={R. Clark Robinson},
year = {2002},
howpublished={\url{https://sites.math.northwestern.edu/~clark/354/2002/perron.pdf}}
}
@MISC{notesonergodictheory,
title = {Notes on ergodic theory},
author={Michael Hochman},
year = {2013},
month = {01},
howpublished={\url{http://math.huji.ac.il/~mhochman/courses/ergodic-theory-2012/notes.final.pdf}}
}
@MISC{introductiontoTF,
title = {{Introduction to Thompson’s group $F$}},
author={Jos\'e Burillo},
howpublished={\url{https://web.mat.upc.edu/pep.burillo/F\%20book.pdf}},
}
@article{10.2307/2000600,
ISSN = {00029947},
URL = {http://www.jstor.org/stable/2000600},
abstract = {We say that a continuous map f of a compact interval to itself is linear Markov if it is piecewise linear, and the set of all fk(x), where k ≥ 0 and x is an endpoint of a linear piece, is finite. We provide an effective classification, up to topological conjugacy, for linear Markov maps and an effective procedure for determining whether such a map is transitive. We also consider expanding Markov maps, partly to motivate the proof of the more complicated linear Markov case.},
author = {Louis Block and Ethan M. Coven},
journal = {Trans. Amer. Math. Soc.},
number = {1},
pages = {297--306},
publisher = {American Mathematical Society},
title = {Topological Conjugacy and Transitivity for a Class of Piecewise Monotone Maps of the Interval},
volume = {300},
year = {1987}
}
% journal = {Transactions of the American Mathematical Society},
@book{sericola2013markov,
title={Markov Chains: Theory and Applications},
author={Sericola, B.},
isbn={9781118731536},
lccn={2013936313},
series={Applied Stochastic Methods Series},
url={https://books.google.com/books?id=tRdwAAAAQBAJ},
year={2013},
publisher={Wiley}
}
@article{10.2307/2044896,
ISSN = {00029939, 10886826},
URL = {http://www.jstor.org/stable/2044896},
abstract = {We give a description of those continuous functions on the interval for which the set of periodic points is dense.},
author = {Marcy Barge and Joe Martin},
journal = {Proc. Amer. Math. Soc. },
number = {4},
pages = {731--735},
publisher = {American Mathematical Society},
title = {Dense Periodicity on the Interval},
volume = {94},
year = {1985}
}
% journal = {Proceedings of the American Mathematical Society},
@article{10.2307/2318254,
ISSN = {00029890, 19300972},
URL = {http://www.jstor.org/stable/2318254},
author = {Tien-Yien Li and James A. Yorke},
journal = {Amer. Math. Monthly},
number = {10},
pages = {985--992},
publisher = {Mathematical Association of America},
title = {Period Three Implies Chaos},
volume = {82},
year = {1975}
}
% journal = {The American Mathematical Monthly},
@article{Sarkovskii1964,
author = {Sarkovskii, A.N.},
year = {1964},
month = {01},
pages = {61-71},
title = {Coexistence of cycles of a continuous map of a line into itself},
volume = {16},
journal = {Ukrain. Mat. \u{Z}.}
}
%journal = {Ukrainian Mathematical Zeitung}
@article{Cleary2002,
author = {Cleary, Sean and Taback, Jennifer},
year = {2002},
month = {09},
pages = {},
title = {Combinatorial properties of Thompson's group {F}},
volume = {356},
journal = {Trans. Amer. Math. Soc.},
doi = {10.2307/3844910}
}
%journal = {Transactions of the American Mathematical Society},