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Anosov diffeomorphisms
| 1. | LIAAD-INESC TEC and Department of Mathematics, School of Technology and Management, Polytechnic Institute of Bragança, Campus de Santa Apolónia, Ap. 1134, 5301-857 Bragança, Portugal |
| 2. | Departamento de Matemática, IME-USP, Caixa Postal 66281, CEP 05315-970 São Paulo, Brazil |
| 3. | LIAAD-INESC TEC and Department of Mathematics, Faculty of Sciences, University of Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal |
| 4. | Warwick Systems Biology & Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom |
References:
| [1] |
R. Adler, C. Tresser and P. A. Worfolk, Topological conjugacy of linear endomorphisms of the 2-torus,, Trans. Amer. Math. Soc., 349 (1997), 1633.
|
| [2] |
J. P. Almeida, A. M. Fisher, A. A. Pinto and D. A. Rand, Anosov and circle diffeomorphisms,, in, (2011), 11. |
| [3] |
J. P. Almeida, A. A. Pinto and D. A. Rand, Renormalization of circle diffeomorphism sequences and Markov sequences,, to appear in, (2012). |
| [4] |
V. I. Arnol'd, Small denominators I: On the mapping of a circle into itself,, Investijia Akad. Nauk. Math., 25 (1961), 21.
|
| [5] |
E. Cawley, The Teichmüller space of an Anosov diffeomorphism of $T^2$,, Inventiones Mathematicae, 112 (1993), 351.
|
| [6] |
P. Coullet and C. Tresser, Itération d'endomorphismes et groupe de renormalisation,, Journal de Physique Colloques, 39 (1978), 5. |
| [7] |
J. Franks, Anosov diffeomorphisms,, in, 14 (1970), 61.
|
| [8] |
E. Ghys, Rigidité différentiable des groupes Fuchsiens,, Publ. IHES, 78 (1993), 163.
|
| [9] |
M. R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations,, Publ. IHES, 49 (1979), 5.
|
| [10] |
Y. Jiang, Teichmüller structures and dual geometric Gibbs type measure theory for continuous potentials,, preprint, (2008), 1. |
| [11] |
Y. Jiang, Metric invariants in dynamical systems,, Journal of Dynamics and Differentiable Equations, 17 (2005), 51.
|
| [12] |
O. Lanford, Renormalization group methods for critical circle mappings with general rotation number,, in, (1987), 532.
|
| [13] |
R. de la Llave, Invariants for smooth conjugacy of hyperbolic dynamical systems II,, Commun. Math. Phys., 109 (1987), 369.
|
| [14] |
A. Manning, There are no new Anosov diffeomorphisms on tori,, Amer. J. Math., 96 (1974), 422.
|
| [15] |
R. Manẽ, "Ergodic Theory and Differentiable Dynamics,", Springer-Verlag, (1987).
|
| [16] |
J. M. Marco, and R. Moriyon, Invariants for Smooth conjugacy of hyperbolic dynamical systems I,, Commun. Math. Phys., 109 (1987), 681.
|
| [17] |
J. M. Marco, and R. Moriyon, Invariants for Smooth conjugacy of hyperbolic dynamical systems III,, Commun. Math. Phys., 112 (1989), 317.
|
| [18] |
H. Masur, Interval exchange transformations and measured foliations,, The Annals of Mathematics. 2nd Ser., 115 (1982), 169.
|
| [19] |
W. de Melo and S. van Strien, "One-dimensional Dynamics,", A series of Modern Surveys in Mathematics, (1993).
|
| [20] |
R. C. Penner and J. L. Harer, "Combinatorics of Train-Tracks,", Princeton University Press, (1992).
|
| [21] |
A. A. Pinto, J. P. Almeida and A. Portela, Golden tilings,, Transactions of the American Mathematical Society, 364 (2012), 2261.
|
| [22] |
A. A. Pinto, J. P. Almeida and D. A. Rand, Anosov and renormalized circle diffeomorphisms,, submitted, (2012), 1. |
| [23] |
A. A. Pinto and D. A. Rand, Train-tracks with $C^{1+}$ self-renormalisable structures,, Journal of Difference Equations and Applications, 16 (2010), 945.
|
| [24] |
A. A. Pinto and D. A. Rand, Solenoid functions for hyperbolic sets on surfaces,, in, (2007), 145.
|
| [25] |
A. A. Pinto and D. A. Rand, Rigidity of hyperbolic sets on surfaces,, J. London Math. Soc., 71 (2004), 481.
|
| [26] |
A. A. Pinto and D. A. Rand, Smoothness of holonomies for codimension 1 hyperbolic dynamics,, Bull. London Math. Soc., 34 (2002), 341.
|
| [27] |
A. A. Pinto and D. A. Rand, Teichmüller spaces and HR structures for hyperbolic surface dynamics,, Ergodic Theory & Dynamical Systems, 22 (2002), 1905.
|
| [28] |
A. A. Pinto and D. A. Rand, Existence, uniqueness and ratio decomposition for Gibbs states via duality,, Ergodic Theory & Dynamical Systems, 21 (2001), 533.
|
| [29] |
A. A. Pinto and D. A. Rand, Characterising rigidity and flexibility of pseudo-Anosov and other transversally laminated dynamical systems on surfaces,, Warwick preprint, (1995). |
| [30] |
A. A. Pinto, D. A. Rand and F. Ferreira, Arc exchange systems and renormalization,, Journal of Difference Equations and Applications, 16 (2010), 347.
|
| [31] |
A. A. Pinto, D. A. Rand and F. Ferreira, Cantor exchange systems and renormalization,, Journal of Differential Equations, 243 (2007), 593.
|
| [32] |
A. A. Pinto, D. A. Rand and F. Ferreira, "Fine structures of hyperbolic diffeomorphisms,", Springer Monographs in Mathematics, (2009).
|
| [33] |
A. A. Pinto and D. Sullivan, The circle and the solenoid,, Dedicated to Anatole Katok On the Occasion of his 60th Birthday, 16 (2006), 463.
|
| [34] |
M. Shub, "Global Stability of Dynamical Systems,", Springer-Verlag, (1987).
|
| [35] |
Ya. Sinai, Markov Partitions and C-diffeomorphisms,, Anal. and Appl., 2 (1968), 70. |
| [36] |
W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces,, Bull. Amer. Math. Soc., 19 (1988), 417.
|
| [37] |
W. Veech, Gauss measures for transformations on the space of interval exchange maps,, The Annals of Mathematics, 115 (1982), 201.
|
| [38] |
R. F. Williams, Expanding attractors,, Publ. I.H.E.S., 43 (1974), 169.
|
| [39] |
R. F. Williams, The "DA" maps of Smale and structural stability,, in, (1970), 329.
|
| [40] |
J. C. Yoccoz, Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne,, Ann. Scient. Éc. Norm. Sup., 17 (1984), 333.
|
show all references
References:
| [1] |
R. Adler, C. Tresser and P. A. Worfolk, Topological conjugacy of linear endomorphisms of the 2-torus,, Trans. Amer. Math. Soc., 349 (1997), 1633.
|
| [2] |
J. P. Almeida, A. M. Fisher, A. A. Pinto and D. A. Rand, Anosov and circle diffeomorphisms,, in, (2011), 11. |
| [3] |
J. P. Almeida, A. A. Pinto and D. A. Rand, Renormalization of circle diffeomorphism sequences and Markov sequences,, to appear in, (2012). |
| [4] |
V. I. Arnol'd, Small denominators I: On the mapping of a circle into itself,, Investijia Akad. Nauk. Math., 25 (1961), 21.
|
| [5] |
E. Cawley, The Teichmüller space of an Anosov diffeomorphism of $T^2$,, Inventiones Mathematicae, 112 (1993), 351.
|
| [6] |
P. Coullet and C. Tresser, Itération d'endomorphismes et groupe de renormalisation,, Journal de Physique Colloques, 39 (1978), 5. |
| [7] |
J. Franks, Anosov diffeomorphisms,, in, 14 (1970), 61.
|
| [8] |
E. Ghys, Rigidité différentiable des groupes Fuchsiens,, Publ. IHES, 78 (1993), 163.
|
| [9] |
M. R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations,, Publ. IHES, 49 (1979), 5.
|
| [10] |
Y. Jiang, Teichmüller structures and dual geometric Gibbs type measure theory for continuous potentials,, preprint, (2008), 1. |
| [11] |
Y. Jiang, Metric invariants in dynamical systems,, Journal of Dynamics and Differentiable Equations, 17 (2005), 51.
|
| [12] |
O. Lanford, Renormalization group methods for critical circle mappings with general rotation number,, in, (1987), 532.
|
| [13] |
R. de la Llave, Invariants for smooth conjugacy of hyperbolic dynamical systems II,, Commun. Math. Phys., 109 (1987), 369.
|
| [14] |
A. Manning, There are no new Anosov diffeomorphisms on tori,, Amer. J. Math., 96 (1974), 422.
|
| [15] |
R. Manẽ, "Ergodic Theory and Differentiable Dynamics,", Springer-Verlag, (1987).
|
| [16] |
J. M. Marco, and R. Moriyon, Invariants for Smooth conjugacy of hyperbolic dynamical systems I,, Commun. Math. Phys., 109 (1987), 681.
|
| [17] |
J. M. Marco, and R. Moriyon, Invariants for Smooth conjugacy of hyperbolic dynamical systems III,, Commun. Math. Phys., 112 (1989), 317.
|
| [18] |
H. Masur, Interval exchange transformations and measured foliations,, The Annals of Mathematics. 2nd Ser., 115 (1982), 169.
|
| [19] |
W. de Melo and S. van Strien, "One-dimensional Dynamics,", A series of Modern Surveys in Mathematics, (1993).
|
| [20] |
R. C. Penner and J. L. Harer, "Combinatorics of Train-Tracks,", Princeton University Press, (1992).
|
| [21] |
A. A. Pinto, J. P. Almeida and A. Portela, Golden tilings,, Transactions of the American Mathematical Society, 364 (2012), 2261.
|
| [22] |
A. A. Pinto, J. P. Almeida and D. A. Rand, Anosov and renormalized circle diffeomorphisms,, submitted, (2012), 1. |
| [23] |
A. A. Pinto and D. A. Rand, Train-tracks with $C^{1+}$ self-renormalisable structures,, Journal of Difference Equations and Applications, 16 (2010), 945.
|
| [24] |
A. A. Pinto and D. A. Rand, Solenoid functions for hyperbolic sets on surfaces,, in, (2007), 145.
|
| [25] |
A. A. Pinto and D. A. Rand, Rigidity of hyperbolic sets on surfaces,, J. London Math. Soc., 71 (2004), 481.
|
| [26] |
A. A. Pinto and D. A. Rand, Smoothness of holonomies for codimension 1 hyperbolic dynamics,, Bull. London Math. Soc., 34 (2002), 341.
|
| [27] |
A. A. Pinto and D. A. Rand, Teichmüller spaces and HR structures for hyperbolic surface dynamics,, Ergodic Theory & Dynamical Systems, 22 (2002), 1905.
|
| [28] |
A. A. Pinto and D. A. Rand, Existence, uniqueness and ratio decomposition for Gibbs states via duality,, Ergodic Theory & Dynamical Systems, 21 (2001), 533.
|
| [29] |
A. A. Pinto and D. A. Rand, Characterising rigidity and flexibility of pseudo-Anosov and other transversally laminated dynamical systems on surfaces,, Warwick preprint, (1995). |
| [30] |
A. A. Pinto, D. A. Rand and F. Ferreira, Arc exchange systems and renormalization,, Journal of Difference Equations and Applications, 16 (2010), 347.
|
| [31] |
A. A. Pinto, D. A. Rand and F. Ferreira, Cantor exchange systems and renormalization,, Journal of Differential Equations, 243 (2007), 593.
|
| [32] |
A. A. Pinto, D. A. Rand and F. Ferreira, "Fine structures of hyperbolic diffeomorphisms,", Springer Monographs in Mathematics, (2009).
|
| [33] |
A. A. Pinto and D. Sullivan, The circle and the solenoid,, Dedicated to Anatole Katok On the Occasion of his 60th Birthday, 16 (2006), 463.
|
| [34] |
M. Shub, "Global Stability of Dynamical Systems,", Springer-Verlag, (1987).
|
| [35] |
Ya. Sinai, Markov Partitions and C-diffeomorphisms,, Anal. and Appl., 2 (1968), 70. |
| [36] |
W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces,, Bull. Amer. Math. Soc., 19 (1988), 417.
|
| [37] |
W. Veech, Gauss measures for transformations on the space of interval exchange maps,, The Annals of Mathematics, 115 (1982), 201.
|
| [38] |
R. F. Williams, Expanding attractors,, Publ. I.H.E.S., 43 (1974), 169.
|
| [39] |
R. F. Williams, The "DA" maps of Smale and structural stability,, in, (1970), 329.
|
| [40] |
J. C. Yoccoz, Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne,, Ann. Scient. Éc. Norm. Sup., 17 (1984), 333.
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