American Institute of Mathematical Sciences

Advanced
January  2007, 18(1): 39-52. doi: 10.3934/dcds.2007.18.39

Examples of Anosov Lie algebras

Meera G. Mainkar 1, and  Cynthia E. Will 2,

1. 

Department of Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada
2. 

FaMAF and CIEM, Universidad Nacional de Córdoba, Haya de la Torre s/n, 5000 Córdoba, Argentina

Received  June 2006 Revised  December 2006 Published  February 2007

We construct new families of examples of (real) Anosov Lie algebras, starting with algebraic units. We also give examples of indecomposable Anosov Lie algebras (not a direct sum of proper Lie ideals) of dimension $13$ and $16$, and we conclude that for every $n \geq 6$ with $n \ne 7$ there exists an indecomposable Anosov Lie algebra of dimension $n$.
Keywords: Anosov diffeomorphisms, hyperbolic automorphisms., nilmanifolds, nilpotent Lie algebras.
Mathematics Subject Classification: Primary: 37D20; Secondary: 22E25, 20F3.
Citation: Meera G. Mainkar, Cynthia E. Will. Examples of Anosov Lie algebras. Discrete & Continuous Dynamical Systems, 2007, 18 (1) : 39-52. doi: 10.3934/dcds.2007.18.39
[1]

Tracy L. Payne. Anosov automorphisms of nilpotent Lie algebras. Journal of Modern Dynamics, 2009, 3 (1) : 121-158. doi: 10.3934/jmd.2009.3.121
[2]

João P. Almeida, Albert M. Fisher, Alberto Adrego Pinto, David A. Rand. Anosov diffeomorphisms. Conference Publications, 2013, 2013 (special) : 837-845. doi: 10.3934/proc.2013.2013.837
[3]

Viorel Niţică. Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups. Discrete & Continuous Dynamical Systems, 2011, 29 (3) : 1197-1204. doi: 10.3934/dcds.2011.29.1197
[4]

Kengo Matsumoto. $ C^* $-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms. Electronic Research Archive, , () : -. doi: 10.3934/era.2021006
[5]

G. Mashevitzky, B. Plotkin and E. Plotkin. Automorphisms of categories of free algebras of varieties. Electronic Research Announcements, 2002, 8: 1-10.

[6]

Peigen Cao, Fang Li, Siyang Liu, Jie Pan. A conjecture on cluster automorphisms of cluster algebras. Electronic Research Archive, 2019, 27: 1-6. doi: 10.3934/era.2019006
[7]

Mark Pollicott. Ergodicity of stable manifolds for nilpotent extensions of Anosov flows. Discrete & Continuous Dynamical Systems, 2002, 8 (3) : 599-604. doi: 10.3934/dcds.2002.8.599
[8]

Hongliang Chang, Yin Chen, Runxuan Zhang. A generalization on derivations of Lie algebras. Electronic Research Archive, 2021, 29 (3) : 2457-2473. doi: 10.3934/era.2020124
[9]

Dominic Veconi. Equilibrium states of almost Anosov diffeomorphisms. Discrete & Continuous Dynamical Systems, 2020, 40 (2) : 767-780. doi: 10.3934/dcds.2020061
[10]

Maria Carvalho. First homoclinic tangencies in the boundary of Anosov diffeomorphisms. Discrete & Continuous Dynamical Systems, 1998, 4 (4) : 765-782. doi: 10.3934/dcds.1998.4.765
[11]

Matthieu Porte. Linear response for Dirac observables of Anosov diffeomorphisms. Discrete & Continuous Dynamical Systems, 2019, 39 (4) : 1799-1819. doi: 10.3934/dcds.2019078
[12]

Christian Bonatti, Nancy Guelman. Axiom A diffeomorphisms derived from Anosov flows. Journal of Modern Dynamics, 2010, 4 (1) : 1-63. doi: 10.3934/jmd.2010.4.1
[13]

Luca Capogna. Optimal regularity for quasilinear equations in stratified nilpotent Lie groups and applications. Electronic Research Announcements, 1996, 2: 60-68.

[14]

Robert L. Griess Jr., Ching Hung Lam. Groups of Lie type, vertex algebras, and modular moonshine. Electronic Research Announcements, 2014, 21: 167-176. doi: 10.3934/era.2014.21.167
[15]

Lennard F. Bakker, Pedro Martins Rodrigues. A profinite group invariant for hyperbolic toral automorphisms. Discrete & Continuous Dynamical Systems, 2012, 32 (6) : 1965-1976. doi: 10.3934/dcds.2012.32.1965
[16]

Zemer Kosloff. On manifolds admitting stable type Ⅲ$_{\textbf1}$ Anosov diffeomorphisms. Journal of Modern Dynamics, 2018, 13: 251-270. doi: 10.3934/jmd.2018020
[17]

Andrey Gogolev, Misha Guysinsky. $C^1$-differentiable conjugacy of Anosov diffeomorphisms on three dimensional torus. Discrete & Continuous Dynamical Systems, 2008, 22 (1&2) : 183-200. doi: 10.3934/dcds.2008.22.183
[18]

Andrey Gogolev. Smooth conjugacy of Anosov diffeomorphisms on higher-dimensional tori. Journal of Modern Dynamics, 2008, 2 (4) : 645-700. doi: 10.3934/jmd.2008.2.645
[19]

Rafael Potrie. Partially hyperbolic diffeomorphisms with a trapping property. Discrete & Continuous Dynamical Systems, 2015, 35 (10) : 5037-5054. doi: 10.3934/dcds.2015.35.5037
[20]

Lorenzo J. Díaz, Todd Fisher. Symbolic extensions and partially hyperbolic diffeomorphisms. Discrete & Continuous Dynamical Systems, 2011, 29 (4) : 1419-1441. doi: 10.3934/dcds.2011.29.1419

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (45)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences