-
Previous Article
Dynamics of $\lambda$-continued fractions and $\beta$-shifts
- DCDS Home
- This Issue
-
Next Article
Glauber dynamics in continuum: A constructive approach to evolution of states
Hyperbolic measures with transverse intersections of stable and unstable manifolds
1. | Faculty of Engineering, Kyushu Institute of Technology, Tobata, Fukuoka 804-8550, Japan |
2. | Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan |
References:
[1] |
V. Araújo and M. J. Pacifico, Large deviations for non-uniformly expanding maps,, J. Stat. Phys., 125 (2006), 411.
doi: 10.1007/s10955-006-9183-y. |
[2] |
L. Barreira and Ya. B. Pesin, "Lyapunov Exponents and Smooth Ergodic Theory,", Univ. Lect. Ser. 23, (2002).
|
[3] |
L. Barreira, Ya. B. Pesin and J. Schmeling, Dimension and product structure of hyperbolic measures,, Ann. of Math., 149 (1999), 755.
doi: 10.2307/121072. |
[4] |
L. R. Bellet and L.-S. Young, Large deviations in non-uniformly hyperbolic dynamical systems,, Ergod. Th. & Dynam. Sys., 28 (2008), 587.
|
[5] |
R. Bowen, Topological entropy for noncompact sets,, Trans. Amer. Math. Soc., 184 (1973), 125.
doi: 10.1090/S0002-9947-1973-0338317-X. |
[6] |
M. Brin, Hölder continuity of invariant distributions,, in, (2001), 91.
|
[7] |
M. Brin, J. Feldman and A. B. Katok, Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents,, Ann. of. Math., 113 (1981), 159.
doi: 10.2307/1971136. |
[8] |
Y. Cao, S. Luzzatto and I. Rios, The boundary of hyperbolicity for Hénon-like families,, Ergod. Th. & Dynam. Sys., 28 (2008), 1049.
|
[9] |
A. Fathi, F. Laudenbach and V. Poénaru, Travaux de Thurston sur les surfaces,, in, 66-67 (1979), 66.
|
[10] |
D. J. Feng, K. S. Lau and J. Wu, Ergodic limits on the conformal repellers,, Adv.Math., 169 (2002), 58.
doi: 10.1006/aima.2001.2054. |
[11] |
O. Frostman, Potential d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions,, Meddel. Lunds Univ. Math. Sem., 3 (1935), 1. Google Scholar |
[12] |
M. Gerber and A. B. Katok, Smooth models of Thurston's pseudo-Anosov maps,, Ann. scient. Éc. Norm. Sup., 15 (1982), 173.
|
[13] |
A. B. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms,, Inst. Hautes Ètudes Sci. Publ. Math., 51 (1980), 137.
doi: 10.1007/BF02684777. |
[14] |
A. B. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,", Cambridge University Press, (1995).
|
[15] |
A. B. Katok and L. Mendoza, Dynamical systems with nonuniformly hyperbolic behavior,, Supplement to, (1995), 659.
|
[16] |
Y. Kifer, Large deviations in dynamical systems and stochastic processes,, Trans. Amer. Math. Soc., 321 (1990), 505.
doi: 10.1090/S0002-9947-1990-1025756-7. |
[17] |
F. Ledrappier and J. M. Strelcyn, A proof of estimation from below in Pesin's entropy formula,, Ergod. Th. & Dynam. Sys., 2 (1982), 203.
|
[18] |
F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms, Part I : Characterization of measures satisfying Pesin's entropy formula,, Ann. of Math., 122 (1985), 509.
doi: 10.2307/1971328. |
[19] |
F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms, Part II: Relations between entropy, exponents and dimension,, Ann. of Math., 122 (1985), 540.
doi: 10.2307/1971329. |
[20] |
R. Mañé, Contributions to the stability conjecture,, Topology, 17 (1978), 383.
doi: 10.1016/0040-9383(78)90005-8. |
[21] |
R. Mañé, "Ergodic Theory and Differentiable Dynamics,", Springer, (1987).
|
[22] |
I. Melbourne and M. Nicol, Large deviations for non-uniformly hyperbolic systems,, Trans. Amer. Math. Soc., 360 (2008), 6661.
doi: 10.1090/S0002-9947-08-04520-0. |
[23] |
S. Orey and S. Pelikan, Deviations of trajectory averages and the defect in Pesin's formula for Anosov diffeomorphisms,, Trans. Amer. Math. Soc., 315 (1989), 741.
doi: 10.2307/2001304. |
[24] |
Ya. B. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents,, Izv. Akd. Nauk SSSR Ser. Mat., 40 (1976), 1332.
|
[25] |
Ya. B. Pesin, "Dimension Theory in Dynamical Systems: Contemporary Views and Applications,", Chicago Lect. Math. Ser., (1997).
|
[26] |
Ya. B. Pesin and H. Weiss, A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions,, J. Stat. Phys., 86 (1997), 233.
doi: 10.1007/BF02180206. |
[27] |
Ya. B. Pesin and H. Weiss, The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples,, Chaos, 7 (1997), 89.
|
[28] |
C.-E. Pfister and W. G. Sullivan, Large deviations estimates for dynamical systems without the specification property. Applications to the $\beta $-shifts,, Nonlinearity, 18 (2005), 237.
doi: 10.1088/0951-7715/18/1/013. |
[29] |
C.-E. Pfister and W. G. Sullivan, On the topological entropy of saturated sets,, Ergod. Th. & Dynam. Sys., 27 (2007), 929.
doi: 10.1017/S0143385706000824. |
[30] |
E. Pujals and M. Sambarino, A sufficient condition for robustly minimal foliations,, Ergod. Th. & Dynam. Sys., 26 (2006), 281.
doi: 10.1017/S0143385705000568. |
[31] |
K. Sakai, N. Sumi and K. Yamamoto, Diffeomorphisms satisfying the specification property,, Proc. Amer. Math. Soc., 138 (2010), 315.
doi: 10.1090/S0002-9939-09-10085-0. |
[32] |
J. Schmeling and H. Weiss, An overview of the dimension theory of dynamical systems,, in, (2001), 429.
|
[33] |
Y. Takahashi, Two aspects of large deviation theory for large time,, in, (1987), 363.
|
[34] |
F. Takens and E. Verbitskiy, Multifractal analysis of local entropies for expansive homeomorphisms with specification,, Commun. Math. Phys., 203 (1999), 593.
doi: 10.1007/s002200050627. |
[35] |
F. Takens and E. Verbitskiy, On the variational principle for the topological entropy of certain noncompact sets,, Ergod. Th. & Dynam. Sys., 23 (2003), 317.
|
[36] |
M. Urbański and C. Wolf, Ergodic Theory of Parabolic Horseshoes,, Commun. Math. Phys., 281 (2008), 711.
doi: 10.1007/s00220-008-0498-1. |
[37] |
L.-S. Young, Dimension, entropy and Lyapunov exponents,, Ergod. Th. & Dynam. Sys., 2 (1982), 109.
|
[38] |
L.-S. Young, Some large deviation results for dynamical systems,, Trans. Amer. Math. Soc., 318 (1990), 525.
doi: 10.2307/2001318. |
show all references
References:
[1] |
V. Araújo and M. J. Pacifico, Large deviations for non-uniformly expanding maps,, J. Stat. Phys., 125 (2006), 411.
doi: 10.1007/s10955-006-9183-y. |
[2] |
L. Barreira and Ya. B. Pesin, "Lyapunov Exponents and Smooth Ergodic Theory,", Univ. Lect. Ser. 23, (2002).
|
[3] |
L. Barreira, Ya. B. Pesin and J. Schmeling, Dimension and product structure of hyperbolic measures,, Ann. of Math., 149 (1999), 755.
doi: 10.2307/121072. |
[4] |
L. R. Bellet and L.-S. Young, Large deviations in non-uniformly hyperbolic dynamical systems,, Ergod. Th. & Dynam. Sys., 28 (2008), 587.
|
[5] |
R. Bowen, Topological entropy for noncompact sets,, Trans. Amer. Math. Soc., 184 (1973), 125.
doi: 10.1090/S0002-9947-1973-0338317-X. |
[6] |
M. Brin, Hölder continuity of invariant distributions,, in, (2001), 91.
|
[7] |
M. Brin, J. Feldman and A. B. Katok, Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents,, Ann. of. Math., 113 (1981), 159.
doi: 10.2307/1971136. |
[8] |
Y. Cao, S. Luzzatto and I. Rios, The boundary of hyperbolicity for Hénon-like families,, Ergod. Th. & Dynam. Sys., 28 (2008), 1049.
|
[9] |
A. Fathi, F. Laudenbach and V. Poénaru, Travaux de Thurston sur les surfaces,, in, 66-67 (1979), 66.
|
[10] |
D. J. Feng, K. S. Lau and J. Wu, Ergodic limits on the conformal repellers,, Adv.Math., 169 (2002), 58.
doi: 10.1006/aima.2001.2054. |
[11] |
O. Frostman, Potential d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions,, Meddel. Lunds Univ. Math. Sem., 3 (1935), 1. Google Scholar |
[12] |
M. Gerber and A. B. Katok, Smooth models of Thurston's pseudo-Anosov maps,, Ann. scient. Éc. Norm. Sup., 15 (1982), 173.
|
[13] |
A. B. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms,, Inst. Hautes Ètudes Sci. Publ. Math., 51 (1980), 137.
doi: 10.1007/BF02684777. |
[14] |
A. B. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,", Cambridge University Press, (1995).
|
[15] |
A. B. Katok and L. Mendoza, Dynamical systems with nonuniformly hyperbolic behavior,, Supplement to, (1995), 659.
|
[16] |
Y. Kifer, Large deviations in dynamical systems and stochastic processes,, Trans. Amer. Math. Soc., 321 (1990), 505.
doi: 10.1090/S0002-9947-1990-1025756-7. |
[17] |
F. Ledrappier and J. M. Strelcyn, A proof of estimation from below in Pesin's entropy formula,, Ergod. Th. & Dynam. Sys., 2 (1982), 203.
|
[18] |
F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms, Part I : Characterization of measures satisfying Pesin's entropy formula,, Ann. of Math., 122 (1985), 509.
doi: 10.2307/1971328. |
[19] |
F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms, Part II: Relations between entropy, exponents and dimension,, Ann. of Math., 122 (1985), 540.
doi: 10.2307/1971329. |
[20] |
R. Mañé, Contributions to the stability conjecture,, Topology, 17 (1978), 383.
doi: 10.1016/0040-9383(78)90005-8. |
[21] |
R. Mañé, "Ergodic Theory and Differentiable Dynamics,", Springer, (1987).
|
[22] |
I. Melbourne and M. Nicol, Large deviations for non-uniformly hyperbolic systems,, Trans. Amer. Math. Soc., 360 (2008), 6661.
doi: 10.1090/S0002-9947-08-04520-0. |
[23] |
S. Orey and S. Pelikan, Deviations of trajectory averages and the defect in Pesin's formula for Anosov diffeomorphisms,, Trans. Amer. Math. Soc., 315 (1989), 741.
doi: 10.2307/2001304. |
[24] |
Ya. B. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents,, Izv. Akd. Nauk SSSR Ser. Mat., 40 (1976), 1332.
|
[25] |
Ya. B. Pesin, "Dimension Theory in Dynamical Systems: Contemporary Views and Applications,", Chicago Lect. Math. Ser., (1997).
|
[26] |
Ya. B. Pesin and H. Weiss, A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions,, J. Stat. Phys., 86 (1997), 233.
doi: 10.1007/BF02180206. |
[27] |
Ya. B. Pesin and H. Weiss, The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples,, Chaos, 7 (1997), 89.
|
[28] |
C.-E. Pfister and W. G. Sullivan, Large deviations estimates for dynamical systems without the specification property. Applications to the $\beta $-shifts,, Nonlinearity, 18 (2005), 237.
doi: 10.1088/0951-7715/18/1/013. |
[29] |
C.-E. Pfister and W. G. Sullivan, On the topological entropy of saturated sets,, Ergod. Th. & Dynam. Sys., 27 (2007), 929.
doi: 10.1017/S0143385706000824. |
[30] |
E. Pujals and M. Sambarino, A sufficient condition for robustly minimal foliations,, Ergod. Th. & Dynam. Sys., 26 (2006), 281.
doi: 10.1017/S0143385705000568. |
[31] |
K. Sakai, N. Sumi and K. Yamamoto, Diffeomorphisms satisfying the specification property,, Proc. Amer. Math. Soc., 138 (2010), 315.
doi: 10.1090/S0002-9939-09-10085-0. |
[32] |
J. Schmeling and H. Weiss, An overview of the dimension theory of dynamical systems,, in, (2001), 429.
|
[33] |
Y. Takahashi, Two aspects of large deviation theory for large time,, in, (1987), 363.
|
[34] |
F. Takens and E. Verbitskiy, Multifractal analysis of local entropies for expansive homeomorphisms with specification,, Commun. Math. Phys., 203 (1999), 593.
doi: 10.1007/s002200050627. |
[35] |
F. Takens and E. Verbitskiy, On the variational principle for the topological entropy of certain noncompact sets,, Ergod. Th. & Dynam. Sys., 23 (2003), 317.
|
[36] |
M. Urbański and C. Wolf, Ergodic Theory of Parabolic Horseshoes,, Commun. Math. Phys., 281 (2008), 711.
doi: 10.1007/s00220-008-0498-1. |
[37] |
L.-S. Young, Dimension, entropy and Lyapunov exponents,, Ergod. Th. & Dynam. Sys., 2 (1982), 109.
|
[38] |
L.-S. Young, Some large deviation results for dynamical systems,, Trans. Amer. Math. Soc., 318 (1990), 525.
doi: 10.2307/2001318. |
[1] |
Shihu Li, Wei Liu, Yingchao Xie. Large deviations for stochastic 3D Leray-$ \alpha $ model with fractional dissipation. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2491-2509. doi: 10.3934/cpaa.2019113 |
[2] |
Christopher Bose, Rua Murray. Minimum 'energy' approximations of invariant measures for nonsingular transformations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 597-615. doi: 10.3934/dcds.2006.14.597 |
[3] |
Zhang Chen, Xiliang Li, Bixiang Wang. Invariant measures of stochastic delay lattice systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3235-3269. doi: 10.3934/dcdsb.2020226 |
[4] |
M. Grasselli, V. Pata. Asymptotic behavior of a parabolic-hyperbolic system. Communications on Pure & Applied Analysis, 2004, 3 (4) : 849-881. doi: 10.3934/cpaa.2004.3.849 |
[5] |
Graziano Crasta, Philippe G. LeFloch. Existence result for a class of nonconservative and nonstrictly hyperbolic systems. Communications on Pure & Applied Analysis, 2002, 1 (4) : 513-530. doi: 10.3934/cpaa.2002.1.513 |
[6] |
Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225 |
[7] |
Boris Kramer, John R. Singler. A POD projection method for large-scale algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 413-435. doi: 10.3934/naco.2016018 |
[8] |
Petra Csomós, Hermann Mena. Fourier-splitting method for solving hyperbolic LQR problems. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 17-46. doi: 10.3934/naco.2018002 |
[9] |
Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258 |
[10] |
Linlin Li, Bedreddine Ainseba. Large-time behavior of matured population in an age-structured model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2561-2580. doi: 10.3934/dcdsb.2020195 |
[11] |
Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 |
[12] |
Sohana Jahan. Discriminant analysis of regularized multidimensional scaling. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 255-267. doi: 10.3934/naco.2020024 |
[13] |
Marian Gidea, Rafael de la Llave, Tere M. Seara. A general mechanism of instability in Hamiltonian systems: Skipping along a normally hyperbolic invariant manifold. Discrete & Continuous Dynamical Systems - A, 2020, 40 (12) : 6795-6813. doi: 10.3934/dcds.2020166 |
[14] |
Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024 |
[15] |
Changpin Li, Zhiqiang Li. Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021023 |
[16] |
Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 |
[17] |
Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Applications of mathematical analysis to problems in theoretical physics. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : i-i. doi: 10.3934/dcdss.2020446 |
[18] |
Martial Agueh, Reinhard Illner, Ashlin Richardson. Analysis and simulations of a refined flocking and swarming model of Cucker-Smale type. Kinetic & Related Models, 2011, 4 (1) : 1-16. doi: 10.3934/krm.2011.4.1 |
[19] |
Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 |
[20] |
Seung-Yeal Ha, Shi Jin. Local sensitivity analysis for the Cucker-Smale model with random inputs. Kinetic & Related Models, 2018, 11 (4) : 859-889. doi: 10.3934/krm.2018034 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]