logo Mathematics Research Reports
Hyperbolicity from contact surgery
Boris Hasselblatt1; Curtis Heberle1
1 Department of Mathematics, Tufts University, Medford, MA 02155, USA
Mathematics Research Reports, Volume 4 (2023), pp. 1-10.

A Dehn surgery on the periodic fiber flow of the unit tangent bundle of a surface produces a uniformly hyperbolic Cantor set for the resulting contact flow.

Received:
Revised:
Published online:
DOI: 10.5802/mrr.14
Classification: 37D20, 57N10
Keywords: Hyperbolic flow, 3-manifold, contact flow, surgery
Boris Hasselblatt 1; Curtis Heberle 1

1 Department of Mathematics, Tufts University, Medford, MA 02155, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{MRR_2023__4__1_0,
     author = {Boris Hasselblatt and Curtis Heberle},
     title = {Hyperbolicity from contact surgery},
     journal = {Mathematics Research Reports},
     pages = {1--10},
     publisher = {MathOA foundation},
     volume = {4},
     year = {2023},
     doi = {10.5802/mrr.14},
     language = {en},
     url = {https://mrr.centre-mersenne.org/articles/10.5802/mrr.14/}
}
TY  - JOUR
AU  - Boris Hasselblatt
AU  - Curtis Heberle
TI  - Hyperbolicity from contact surgery
JO  - Mathematics Research Reports
PY  - 2023
SP  - 1
EP  - 10
VL  - 4
PB  - MathOA foundation
UR  - https://mrr.centre-mersenne.org/articles/10.5802/mrr.14/
DO  - 10.5802/mrr.14
LA  - en
ID  - MRR_2023__4__1_0
ER  - 
%0 Journal Article
%A Boris Hasselblatt
%A Curtis Heberle
%T Hyperbolicity from contact surgery
%J Mathematics Research Reports
%D 2023
%P 1-10
%V 4
%I MathOA foundation
%U https://mrr.centre-mersenne.org/articles/10.5802/mrr.14/
%R 10.5802/mrr.14
%G en
%F MRR_2023__4__1_0
Boris Hasselblatt; Curtis Heberle. Hyperbolicity from contact surgery. Mathematics Research Reports, Volume 4 (2023), pp. 1-10. doi : 10.5802/mrr.14. https://mrr.centre-mersenne.org/articles/10.5802/mrr.14/

[1] Robert Burton; Robert W. Easton Ergodicity of linked twist maps, Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979) (Lecture Notes in Math.), Volume 819, Springer, Berlin (1980), pp. 35-49 | DOI | MR | Zbl

[2] Vincent Colin; Pierre Dehornoy; Ana Rechtman On the existence of supporting broken book decompositions for contact forms in dimension 3, 2020 | arXiv

[3] Robert L. Devaney Subshifts of finite type in linked twist mappings, Proc. Amer. Math. Soc., Volume 71 (1978) no. 2, pp. 334-338 | DOI | MR | Zbl

[4] Robert L. Devaney Linked twist mappings are almost Anosov, Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979) (Lecture Notes in Math.), Volume 819, Springer, Berlin (1980), pp. 121-145 | DOI | MR | Zbl

[5] Todd Fisher; Boris Hasselblatt Hyperbolic flows, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich, 2019 | DOI

[6] Patrick Foulon; Boris Hasselblatt Contact Anosov flows on hyperbolic 3-manifolds, Geom. Topol., Volume 17 (2013) no. 2, pp. 1225-1252 | DOI | MR | Zbl

[7] Patrick Foulon; Boris Hasselblatt; Anne Vaugon Orbit growth of contact structures after surgery, Ann. H. Lebesgue, Volume 4 (2021), pp. 1103-1141 | DOI | Numdam | MR | Zbl

[8] Matthew Nicol A Bernoulli toral linked twist map without positive Lyapunov exponents, Proc. Amer. Math. Soc., Volume 124 (1996) no. 4, pp. 1253-1263 | DOI | MR | Zbl

[9] Matthew Nicol Stochastic stability of Bernoulli toral linked twist maps of finite and infinite entropy, Ergodic Theory Dynam. Systems, Volume 16 (1996) no. 3, pp. 493-518 | DOI | MR | Zbl

[10] Feliks Przytycki Ergodicity of toral linked twist mappings, Ann. Sci. École Norm. Sup. (4), Volume 16 (1983) no. 3, p. 345-354 (1984) | DOI | Numdam | MR | Zbl

[11] J. Springham; R. Sturman Polynomial decay of correlations in linked-twist maps, Ergodic Theory Dynam. Systems, Volume 34 (2014) no. 5, pp. 1724-1746 | DOI | MR | Zbl

[12] James Springham Ergodic properties of linked-twist maps, 2008 | arXiv

[13] James Springham; Stephen Wiggins Bernoulli linked-twist maps in the plane, Dyn. Syst., Volume 25 (2010) no. 4, pp. 483-499 | DOI | MR | Zbl

[14] Rob Sturman; Julio M. Ottino; Stephen Wiggins The mathematical foundations of mixing, Cambridge Monographs on Applied and Computational Mathematics, 22, Cambridge University Press, Cambridge, 2006, xx+281 pages (The linked twist map as a paradigm in applications: micro to macro, fluids to solids) | DOI | MR

[15] Maciej Wojtkowski Linked twist mappings have the K-property, Nonlinear dynamics (Internat. Conf., New York, 1979) (Ann. New York Acad. Sci.), Volume 357, New York Acad. Sci., New York, 1980, pp. 65-76 | MR | Zbl

Cited by Sources: