American Institute of Mathematical Sciences

Advanced
April  2008, 2(2): 359-373. doi: 10.3934/jmd.2008.2.359

$C^1$-generic conservative diffeomorphisms have trivial centralizer

Christian Bonatti 1, , Sylvain Crovisier 2, and  Amie Wilkinson 3,

1. 

Université de Bourgogne, Laboratoire de Topologie, UMR 5584 du CNRS, BP 47 870, 21078 Dijon Cedex
2. 

CNRS - Laboratoire Analyse, Géométrie et Applications UMR 7539, Institut Galilée, Université Paris 13, 99 Avenue J.-B. Clément, 934390 Villetaneuse, France
3. 

Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, United States

Revised  October 2007 Published  January 2008

We prove that the spaces of $C^1$ symplectomorphisms and of $C^1$ volume-preserving diffeomorphisms of connected manifolds contain residual subsets of diffeomorphisms whose centralizers are trivial.
Keywords: Trivial centralizer, trivial symmetries, $C^1$ generic properties..
Mathematics Subject Classification: Primary: 37C85, Secondary: 37D4.
Citation: Christian Bonatti, Sylvain Crovisier, Amie Wilkinson. $C^1$-generic conservative diffeomorphisms have trivial centralizer. Journal of Modern Dynamics, 2008, 2 (2) : 359-373. doi: 10.3934/jmd.2008.2.359
[1]

Christian Bonatti, Sylvain Crovisier and Amie Wilkinson. The centralizer of a $C^1$-generic diffeomorphism is trivial. Electronic Research Announcements, 2008, 15: 33-43. doi: 10.3934/era.2008.15.33
[2]

Raquel Ribeiro. Hyperbolicity and types of shadowing for $C^1$ generic vector fields. Discrete & Continuous Dynamical Systems - A, 2014, 34 (7) : 2963-2982. doi: 10.3934/dcds.2014.34.2963
[3]

Katsutoshi Shinohara. On the index problem of $C^1$-generic wild homoclinic classes in dimension three. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 913-940. doi: 10.3934/dcds.2011.31.913
[4]

Rafael Ortega. Trivial dynamics for a class of analytic homeomorphisms of the plane. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 651-659. doi: 10.3934/dcdsb.2008.10.651
[5]

S. Yu. Pilyugin, Kazuhiro Sakai, O. A. Tarakanov. Transversality properties and $C^1$-open sets of diffeomorphisms with weak shadowing. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 871-882. doi: 10.3934/dcds.2006.16.871
[6]

Francisco Braun, Jaume Llibre, Ana Cristina Mereu. Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5245-5255. doi: 10.3934/dcds.2016029
[7]

Olof Heden, Fabio Pasticci, Thomas Westerbäck. On the existence of extended perfect binary codes with trivial symmetry group. Advances in Mathematics of Communications, 2009, 3 (3) : 295-309. doi: 10.3934/amc.2009.3.295
[8]

Kung-Ching Chang, Zhi-Qiang Wang, Tan Zhang. On a new index theory and non semi-trivial solutions for elliptic systems. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 809-826. doi: 10.3934/dcds.2010.28.809
[9]

Wouter Castryck, Marco Streng, Damiano Testa. Curves in characteristic $2$ with non-trivial $2$-torsion. Advances in Mathematics of Communications, 2014, 8 (4) : 479-495. doi: 10.3934/amc.2014.8.479
[10]

Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky. Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4619-4635. doi: 10.3934/dcds.2016001
[11]

Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky. Corrigendum to "Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology". Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4585-4586. doi: 10.3934/dcds.2017196
[12]

Genni Fragnelli, Paolo Nistri, Duccio Papini. Corrigendum: Nnon-trivial non-negative periodic solutions of a system of doubly degenerate parabolic equations with nonlocal terms. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3831-3834. doi: 10.3934/dcds.2013.33.3831
[13]

Rui Huang, Yifu Wang, Yuanyuan Ke. Existence of non-trivial nonnegative periodic solutions for a class of degenerate parabolic equations with nonlocal terms. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 1005-1014. doi: 10.3934/dcdsb.2005.5.1005
[14]

Genni Fragnelli, Paolo Nistri, Duccio Papini. Non-trivial non-negative periodic solutions of a system of doubly degenerate parabolic equations with nonlocal terms. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 35-64. doi: 10.3934/dcds.2011.31.35
[15]

Jana Rodriguez Hertz. Some advances on generic properties of the Oseledets splitting. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4323-4339. doi: 10.3934/dcds.2013.33.4323
[16]

Keonhee Lee, Kazumine Moriyasu, Kazuhiro Sakai. $C^1$-stable shadowing diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2008, 22 (3) : 683-697. doi: 10.3934/dcds.2008.22.683
[17]

Lan Wen. A uniform $C^1$ connecting lemma. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 257-265. doi: 10.3934/dcds.2002.8.257
[18]

Piotr Kościelniak, Marcin Mazur. On $C^0$ genericity of various shadowing properties. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 523-530. doi: 10.3934/dcds.2005.12.523
[19]

Hermann Köenig, Vitali Milman. Derivative and entropy: the only derivations from $C^1(RR)$ to $C(RR)$. Electronic Research Announcements, 2011, 18: 54-60. doi: 10.3934/era.2011.18.54
[20]

David Galindo, Javier Herranz, Eike Kiltz. On the generic construction of identity-based signatures with additional properties. Advances in Mathematics of Communications, 2010, 4 (4) : 453-483. doi: 10.3934/amc.2010.4.453

2019 Impact Factor: 0.465

Tools

Metrics

  • PDF downloads (31)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences