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Generic 3dimensional volumepreserving diffeomorphisms with superexponential growth of number of periodic orbits
1.  Mathematics 25337, California Institute of Technology, Pasadena, CA, 91106, United States 
2.  Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4, Canada 
[1] 
Roland Zweimüller. Asymptotic orbit complexity of infinite measure preserving transformations. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 353366. doi: 10.3934/dcds.2006.15.353 
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Rui Kuang, Xiangdong Ye. The return times set and mixing for measure preserving transformations. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 817827. doi: 10.3934/dcds.2007.18.817 
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S. Eigen, A. B. Hajian, V. S. Prasad. Universal skyscraper templates for infinite measure preserving transformations. Discrete and Continuous Dynamical Systems, 2006, 16 (2) : 343360. doi: 10.3934/dcds.2006.16.343 
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Wenxiang Sun, Yun Yang. Hyperbolic periodic points for chain hyperbolic homoclinic classes. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 39113925. doi: 10.3934/dcds.2016.36.3911 
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Tatiane C. Batista, Juliano S. Gonschorowski, Fábio A. Tal. Density of the set of endomorphisms with a maximizing measure supported on a periodic orbit. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 33153326. doi: 10.3934/dcds.2015.35.3315 
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Christian Bonatti, Lorenzo J. Díaz, Todd Fisher. Superexponential growth of the number of periodic orbits inside homoclinic classes. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 589604. doi: 10.3934/dcds.2008.20.589 
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Zhihong Xia. Homoclinic points and intersections of Lagrangian submanifold. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 243253. doi: 10.3934/dcds.2000.6.243 
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Benjamin Wincure, Alejandro D. Rey. Growth regimes in phase ordering transformations. Discrete and Continuous Dynamical Systems  B, 2007, 8 (3) : 623648. doi: 10.3934/dcdsb.2007.8.623 
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Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 63096330. doi: 10.3934/dcds.2020281 
[10] 
Vadim Yu. Kaloshin and Brian R. Hunt. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II. Electronic Research Announcements, 2001, 7: 2836. 
[11] 
Vadim Yu. Kaloshin and Brian R. Hunt. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I. Electronic Research Announcements, 2001, 7: 1727. 
[12] 
Oksana Koltsova, Lev Lerman. Hamiltonian dynamics near nontransverse homoclinic orbit to saddlefocus equilibrium. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 883913. doi: 10.3934/dcds.2009.25.883 
[13] 
Benoît Grébert, Tiphaine Jézéquel, Laurent Thomann. Dynamics of KleinGordon on a compact surface near a homoclinic orbit. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 34853510. doi: 10.3934/dcds.2014.34.3485 
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Shigui Ruan, Junjie Wei, Jianhong Wu. Bifurcation from a homoclinic orbit in partial functional differential equations. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 12931322. doi: 10.3934/dcds.2003.9.1293 
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W.J. Beyn, Y.K Zou. Discretizations of dynamical systems with a saddlenode homoclinic orbit. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 351365. doi: 10.3934/dcds.1996.2.351 
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K. H. Kim, F. W. Roush and J. B. Wagoner. Inert actions on periodic points. Electronic Research Announcements, 1997, 3: 5562. 
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Charles Pugh, Michael Shub. Periodic points on the $2$sphere. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 11711182. doi: 10.3934/dcds.2014.34.1171 
[18] 
Sonja Hohloch. Transport, flux and growth of homoclinic Floer homology. Discrete and Continuous Dynamical Systems, 2012, 32 (10) : 35873620. doi: 10.3934/dcds.2012.32.3587 
[19] 
Peter Giesl. Converse theorem on a global contraction metric for a periodic orbit. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 53395363. doi: 10.3934/dcds.2019218 
[20] 
Roland Gunesch, Anatole Katok. Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 6188. doi: 10.3934/dcds.2000.6.61 
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