-
Previous Article
Brownian-time Brownian motion SIEs on $\mathbb{R}_{+}$ × $\mathbb{R}^d$: Ultra regular direct and lattice-limits solutions and fourth order SPDEs links
- DCDS Home
- This Issue
- Next Article
Pinching conditions, linearization and regularity of Axiom A flows
1. | School of Mathematics and Statistics, University of Western Australia, 35 Stirling Hwy, Crawley WA 6009, Australia |
References:
[1] |
N. Anantharaman, Precise counting results for closed orbits of Anosov flows, Ann. Scient. Éc. Norm. Sup., 33 (2000), 33-56. |
[2] |
R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math., 95 (1973), 429-460.
doi: 10.2307/2373793. |
[3] |
R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math., 29 (1975), 181-202.
doi: 10.1007/BF01389848. |
[4] |
D. Dolgopyat, On decay of correlations in Anosov flows, Ann. of Math., 147 (1998), 357-390.
doi: 10.2307/121012. |
[5] |
M. Guysinsky, B. Hasselblatt and V. Rayskin, Differentiability of the Hartman-Grobman linearization, Discr. Cont. Dyn. Syst., 9 (2003), 979-984. |
[6] |
B. Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergod. Th. & Dynam. Sys., 14 (1994), 645-666. |
[7] |
B. Hasselblatt, Regularity of the Anosov splitting, Ergod. Th. & Dynam. Sys., 17 (1997), 169-172.
doi: 10.1017/S0143385797069757. |
[8] |
M. Hirsch and C. Pugh, Smoothness of horocycle foliations, J. Differential Geometry, 10 (1975), 225-238. |
[9] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds,'' Springer Lecture Notes in Mathematics, 583 1977. |
[10] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,'' Cambridge Univ. Press, Cambridge, 1995. |
[11] |
W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astéerisque, 187-188 (1990), 268 pp. |
[12] |
Ya. Pesin, "Lectures on Partial Hyperbolicity and Stable Ergodicity,'' European Mathematical Society, Zürich, 2004. |
[13] |
V. Petkov and L. Stoyanov, Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function, Analysis and PDE, 3 (2010), 427-489. |
[14] |
V. Petkov and L. Stoyanov, Correlations for pairs of closed trajectories in open billiards, Nonlinearity, 22 (2009), 2657-2679.
doi: 10.1088/0951-7715/22/11/005. |
[15] |
V. Petkov and L. Stoyanov, Distribution of periods of closed trajectories in exponentially shrinking intervals, Commun. Math. Phys., 310 (2012), 675-704.
doi: 10.1007/s00220-012-1419-x. |
[16] |
M. Pollicott and R. Sharp, Exponential error terms for growth functions of negatively curved surfaces, Amer. J. Math., 120 (1998), 1019-1042.
doi: 10.1353/ajm.1998.0041. |
[17] |
M. Pollicott and R. Sharp, Asymptotic expansions for closed orbits in homology classes, Geom. Dedicata, 87 (2001), 123-160.
doi: 10.1023/A:1012097314447. |
[18] |
M. Pollicott and R. Sharp, Correlations for pairs of closed geodesics, Invent. Math., 163 (2006), 1-24.
doi: 10.1007/s00222-004-0427-7. |
[19] |
C. Pugh and M. Shub, Linearization of normally hyperbolic diffeomorphisms and flows, Invent. Math., 10 (1970), 187-198.
doi: 10.1007/BF01403247. |
[20] |
C. Pugh, M. Shub and A. Wilkinson, Hölder foliations, Duke Math. J., 86 (1997), 517-546; Correction: Duke Math. J., 105 (2000), 105-106.
doi: 10.1215/S0012-7094-97-08616-6. |
[21] |
L. Stoyanov, Spectra of Ruelle transfer operators for Axiom A flows, Nonlinearity, 24 (2011), 1089-1120.
doi: 10.1088/0951-7715/24/4/005. |
[22] |
L. Stoyanov, Non-integrability of open billiard flows and Dolgopyat type estimates, Ergod. Th. & Dynam. Sys., 32 (2012), 295-313.
doi: 10.1017/S0143385710000933. |
show all references
References:
[1] |
N. Anantharaman, Precise counting results for closed orbits of Anosov flows, Ann. Scient. Éc. Norm. Sup., 33 (2000), 33-56. |
[2] |
R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math., 95 (1973), 429-460.
doi: 10.2307/2373793. |
[3] |
R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math., 29 (1975), 181-202.
doi: 10.1007/BF01389848. |
[4] |
D. Dolgopyat, On decay of correlations in Anosov flows, Ann. of Math., 147 (1998), 357-390.
doi: 10.2307/121012. |
[5] |
M. Guysinsky, B. Hasselblatt and V. Rayskin, Differentiability of the Hartman-Grobman linearization, Discr. Cont. Dyn. Syst., 9 (2003), 979-984. |
[6] |
B. Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergod. Th. & Dynam. Sys., 14 (1994), 645-666. |
[7] |
B. Hasselblatt, Regularity of the Anosov splitting, Ergod. Th. & Dynam. Sys., 17 (1997), 169-172.
doi: 10.1017/S0143385797069757. |
[8] |
M. Hirsch and C. Pugh, Smoothness of horocycle foliations, J. Differential Geometry, 10 (1975), 225-238. |
[9] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds,'' Springer Lecture Notes in Mathematics, 583 1977. |
[10] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,'' Cambridge Univ. Press, Cambridge, 1995. |
[11] |
W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astéerisque, 187-188 (1990), 268 pp. |
[12] |
Ya. Pesin, "Lectures on Partial Hyperbolicity and Stable Ergodicity,'' European Mathematical Society, Zürich, 2004. |
[13] |
V. Petkov and L. Stoyanov, Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function, Analysis and PDE, 3 (2010), 427-489. |
[14] |
V. Petkov and L. Stoyanov, Correlations for pairs of closed trajectories in open billiards, Nonlinearity, 22 (2009), 2657-2679.
doi: 10.1088/0951-7715/22/11/005. |
[15] |
V. Petkov and L. Stoyanov, Distribution of periods of closed trajectories in exponentially shrinking intervals, Commun. Math. Phys., 310 (2012), 675-704.
doi: 10.1007/s00220-012-1419-x. |
[16] |
M. Pollicott and R. Sharp, Exponential error terms for growth functions of negatively curved surfaces, Amer. J. Math., 120 (1998), 1019-1042.
doi: 10.1353/ajm.1998.0041. |
[17] |
M. Pollicott and R. Sharp, Asymptotic expansions for closed orbits in homology classes, Geom. Dedicata, 87 (2001), 123-160.
doi: 10.1023/A:1012097314447. |
[18] |
M. Pollicott and R. Sharp, Correlations for pairs of closed geodesics, Invent. Math., 163 (2006), 1-24.
doi: 10.1007/s00222-004-0427-7. |
[19] |
C. Pugh and M. Shub, Linearization of normally hyperbolic diffeomorphisms and flows, Invent. Math., 10 (1970), 187-198.
doi: 10.1007/BF01403247. |
[20] |
C. Pugh, M. Shub and A. Wilkinson, Hölder foliations, Duke Math. J., 86 (1997), 517-546; Correction: Duke Math. J., 105 (2000), 105-106.
doi: 10.1215/S0012-7094-97-08616-6. |
[21] |
L. Stoyanov, Spectra of Ruelle transfer operators for Axiom A flows, Nonlinearity, 24 (2011), 1089-1120.
doi: 10.1088/0951-7715/24/4/005. |
[22] |
L. Stoyanov, Non-integrability of open billiard flows and Dolgopyat type estimates, Ergod. Th. & Dynam. Sys., 32 (2012), 295-313.
doi: 10.1017/S0143385710000933. |
[1] |
Jeremy LeCrone, Yuanzhen Shao, Gieri Simonett. The surface diffusion and the Willmore flow for uniformly regular hypersurfaces. Discrete and Continuous Dynamical Systems - S, 2020, 13 (12) : 3503-3524. doi: 10.3934/dcdss.2020242 |
[2] |
Stefanie Hittmeyer, Bernd Krauskopf, Hinke M. Osinga, Katsutoshi Shinohara. How to identify a hyperbolic set as a blender. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6815-6836. doi: 10.3934/dcds.2020295 |
[3] |
Dung Le. On the regular set of BMO weak solutions to $p$-Laplacian strongly coupled nonregular elliptic systems. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : 3245-3265. doi: 10.3934/dcdsb.2014.19.3245 |
[4] |
Van Cyr, John Franks, Bryna Kra, Samuel Petite. Distortion and the automorphism group of a shift. Journal of Modern Dynamics, 2018, 13: 147-161. doi: 10.3934/jmd.2018015 |
[5] |
Światosław R. Gal, Jarek Kędra. On distortion in groups of homeomorphisms. Journal of Modern Dynamics, 2011, 5 (3) : 609-622. doi: 10.3934/jmd.2011.5.609 |
[6] |
Sheldon Newhouse. Distortion estimates for planar diffeomorphisms. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 345-412. doi: 10.3934/dcds.2008.22.345 |
[7] |
Tong Li, Sunčica Čanić. Critical thresholds in a quasilinear hyperbolic model of blood flow. Networks and Heterogeneous Media, 2009, 4 (3) : 527-536. doi: 10.3934/nhm.2009.4.527 |
[8] |
Zhengchao Ji. Cylindrical estimates for mean curvature flow in hyperbolic spaces. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1199-1211. doi: 10.3934/cpaa.2021016 |
[9] |
Tong Li, Kun Zhao. On a quasilinear hyperbolic system in blood flow modeling. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 333-344. doi: 10.3934/dcdsb.2011.16.333 |
[10] |
Francois Ledrappier and Omri Sarig. Invariant measures for the horocycle flow on periodic hyperbolic surfaces. Electronic Research Announcements, 2005, 11: 89-94. |
[11] |
Zheng Yin, Ercai Chen. Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6581-6597. doi: 10.3934/dcds.2016085 |
[12] |
Richard Sharp. Distortion and entropy for automorphisms of free groups. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 347-363. doi: 10.3934/dcds.2010.26.347 |
[13] |
Yifei Lou, Sung Ha Kang, Stefano Soatto, Andrea L. Bertozzi. Video stabilization of atmospheric turbulence distortion. Inverse Problems and Imaging, 2013, 7 (3) : 839-861. doi: 10.3934/ipi.2013.7.839 |
[14] |
Steinar Evje, Kenneth H. Karlsen. Hyperbolic-elliptic models for well-reservoir flow. Networks and Heterogeneous Media, 2006, 1 (4) : 639-673. doi: 10.3934/nhm.2006.1.639 |
[15] |
Anke D. Pohl. Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2173-2241. doi: 10.3934/dcds.2014.34.2173 |
[16] |
Jiaxi Huang, Youde Wang, Lifeng Zhao. Equivariant Schrödinger map flow on two dimensional hyperbolic space. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 4379-4425. doi: 10.3934/dcds.2020184 |
[17] |
Stefano Bianchini. On the shift differentiability of the flow generated by a hyperbolic system of conservation laws. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 329-350. doi: 10.3934/dcds.2000.6.329 |
[18] |
Ali Unver, Christian Ringhofer, Dieter Armbruster. A hyperbolic relaxation model for product flow in complex production networks. Conference Publications, 2009, 2009 (Special) : 790-799. doi: 10.3934/proc.2009.2009.790 |
[19] |
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 and Continuous Dynamical Systems, 2016, 36 (9) : 4619-4635. doi: 10.3934/dcds.2016001 |
[20] |
Rafael O. Ruggiero. Shadowing of geodesics, weak stability of the geodesic flow and global hyperbolic geometry. Discrete and Continuous Dynamical Systems, 2006, 14 (2) : 365-383. doi: 10.3934/dcds.2006.14.365 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]