-
Previous Article
The automorphism group of a minimal shift of stretched exponential growth
- JMD Home
- This Volume
-
Next Article
Boundary unitary representations—right-angled hyperbolic buildings
Smooth diffeomorphisms with homogeneous spectrum and disjointness of convolutions
1. | Department of Mathematics, University of Hamburg, Bundesstraße 55, 20146 Hamburg, Germany |
References:
[1] |
O. N. Ageev, On ergodic transformations with homogeneous spectrum, J. Dynam. Control Systems, 5 (1999), 149-152.
doi: 10.1023/A:1021701019156. |
[2] |
O. N. Ageev, The homogeneous spectrum problem in ergodic theory, Invent. Math., 160 (2005), 417-446.
doi: 10.1007/s00222-004-0422-z. |
[3] |
D. V. Anosov and A. Katok, New examples in smooth ergodic theory. Ergodic diffeomorphisms, Trudy Moskov. Mat. Obšč., 23 (1970), 3-36. |
[4] |
M. Benhenda, Non-standard smooth realization of shifts on the torus, J. Modern Dynamics, 7 (2013), 329-367. |
[5] |
R. Berndt, Einführung in die symplektische Geometrie, Friedr. Vieweg & Sohn, Braunschweig, 1998.
doi: 10.1007/978-3-322-80215-6. |
[6] |
F. Blanchard and M. Lemańczyk, Measure-preserving diffeomorphisms with an arbitrary spectral multiplicity, Topol. Methods Nonlinear Anal., 1 (1993), 275-294. |
[7] |
I. P. Cornfeld, S. V. Fomin and Ya. G. Sinaĭ, Ergodic Theory, Springer-Verlag, New York, 1982.
doi: 10.1007/978-1-4615-6927-5. |
[8] |
G. M. Constantine and T. H. Savits, A multivariate Faà di Bruno formula with applications, Trans. Amer. Math. Soc., 348 (1996), 503-520.
doi: 10.1090/S0002-9947-96-01501-2. |
[9] |
A. Danilenko, A survey on spectral multiplicities of ergodic actions, Ergodic Theory Dynam. Systems, 33 (2013), 81-117.
doi: 10.1017/S0143385711000800. |
[10] |
B. Fayad and A. Katok, Constructions in elliptic dynamics, Ergodic Theory Dynam. Systems, 24 (2004), 1477-1520.
doi: 10.1017/S0143385703000798. |
[11] |
B. Fayad and M. Saprykina, Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary, Ann. Sci. École Norm. Sup. (4), 38 (2005), 339-364.
doi: 10.1016/j.ansens.2005.03.004. |
[12] |
B. Fayad, M. Saprykina and A. Windsor, Non-standard smooth realizations of Liouville rotations, Ergodic Theory Dynam. Systems, 27 (2007), 1803-1818.
doi: 10.1017/S0143385707000314. |
[13] |
R. Gunesch and A. Katok, Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure, Discrete Contin. Dynam. Systems, 6 (2000), 61-88.
doi: 10.3934/dcds.2000.6.61. |
[14] |
G. R. Goodson, A survey of recent results in the spectral theory of ergodic dynamical systems, J. Dynam. Control Systems, 5 (1999), 173-226.
doi: 10.1023/A:1021726902801. |
[15] |
B. Hasselblatt and A. Katok, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511809187. |
[16] |
A. Katok, Bernoulli diffeomorphisms on surfaces, Ann. of Math. (2), 110 (1979), 529-547.
doi: 10.2307/1971237. |
[17] |
A. Katok, Combinatorical Constructions in Ergodic Theory and Dynamics, American Mathematical Society, Providence, RI, 2003.
doi: 10.1090/ulect/030. |
[18] |
J. Kwiatkowski and M. Lemańczyk, On the multiplicity function of ergodic group extensions. II, Studia Math., 116 (1995), 207-214. |
[19] |
A. Kriegl and P. Michor, The Convenient Setting of Global Analysis, American Mathematical Society, Providence, RI, 1997.
doi: 10.1090/surv/053. |
[20] |
A. Katok and A. Stepin, Approximations in ergodic theory, Russ. Math. Surveys, 22 (1967), 77-102.
doi: 10.1070/RM1967v022n05ABEH001227. |
[21] |
A. Katok and A. Stepin, Metric properties of measure preserving homeomorphisms, Russ. Math. Surveys, 25 (1970), 191-220.
doi: 10.1070/RM1970v025n02ABEH003793. |
[22] |
M. G. Nadkarni, Spectral Theory of Dynamical Systems, Birkhäuser Verlag, Basel, 1998.
doi: 10.1007/978-3-0348-8841-7. |
[23] |
H. Omori, Infinite Dimensional Lie Transformation Groups, Springer-Verlag, Berlin-New York, 1974. |
[24] |
V. I. Oseledets, An automorphism with simple continuous spectrum not having the group property, Mat. Zametki, 5 (1969), 323-326. |
[25] |
V. V. Ryzhikov, Transformations having homogeneous spectra, J. Dynam. Control Systems, 5 (1999), 145-148.
doi: 10.1023/A:1021748902318. |
[26] |
V. V. Ryzhikov, Homogeneous spectrum, disjointness of convolutions and mixing properties of dynamical systems, Selected Russian Math., 1 (1999), 13-24. |
[27] |
V. V. Ryzhikov, On the spectral and mixing properties of rank-1 constructions in ergodic theory, Doklady Mathematics, 74 (2006), 545-547. |
[28] |
A. M. Stepin, Properties of spectra of ergodic dynamical systems with locally compact time, Dokl. Akad. Nauk SSSR, 169 (1966), 773-776. |
[29] |
A. M. Stepin, Spectral properties of generic dynamical systems, Math. USSR Izv., 29 (1987), 159-192.
doi: 10.1070/IM1987v029n01ABEH000965. |
show all references
References:
[1] |
O. N. Ageev, On ergodic transformations with homogeneous spectrum, J. Dynam. Control Systems, 5 (1999), 149-152.
doi: 10.1023/A:1021701019156. |
[2] |
O. N. Ageev, The homogeneous spectrum problem in ergodic theory, Invent. Math., 160 (2005), 417-446.
doi: 10.1007/s00222-004-0422-z. |
[3] |
D. V. Anosov and A. Katok, New examples in smooth ergodic theory. Ergodic diffeomorphisms, Trudy Moskov. Mat. Obšč., 23 (1970), 3-36. |
[4] |
M. Benhenda, Non-standard smooth realization of shifts on the torus, J. Modern Dynamics, 7 (2013), 329-367. |
[5] |
R. Berndt, Einführung in die symplektische Geometrie, Friedr. Vieweg & Sohn, Braunschweig, 1998.
doi: 10.1007/978-3-322-80215-6. |
[6] |
F. Blanchard and M. Lemańczyk, Measure-preserving diffeomorphisms with an arbitrary spectral multiplicity, Topol. Methods Nonlinear Anal., 1 (1993), 275-294. |
[7] |
I. P. Cornfeld, S. V. Fomin and Ya. G. Sinaĭ, Ergodic Theory, Springer-Verlag, New York, 1982.
doi: 10.1007/978-1-4615-6927-5. |
[8] |
G. M. Constantine and T. H. Savits, A multivariate Faà di Bruno formula with applications, Trans. Amer. Math. Soc., 348 (1996), 503-520.
doi: 10.1090/S0002-9947-96-01501-2. |
[9] |
A. Danilenko, A survey on spectral multiplicities of ergodic actions, Ergodic Theory Dynam. Systems, 33 (2013), 81-117.
doi: 10.1017/S0143385711000800. |
[10] |
B. Fayad and A. Katok, Constructions in elliptic dynamics, Ergodic Theory Dynam. Systems, 24 (2004), 1477-1520.
doi: 10.1017/S0143385703000798. |
[11] |
B. Fayad and M. Saprykina, Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary, Ann. Sci. École Norm. Sup. (4), 38 (2005), 339-364.
doi: 10.1016/j.ansens.2005.03.004. |
[12] |
B. Fayad, M. Saprykina and A. Windsor, Non-standard smooth realizations of Liouville rotations, Ergodic Theory Dynam. Systems, 27 (2007), 1803-1818.
doi: 10.1017/S0143385707000314. |
[13] |
R. Gunesch and A. Katok, Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure, Discrete Contin. Dynam. Systems, 6 (2000), 61-88.
doi: 10.3934/dcds.2000.6.61. |
[14] |
G. R. Goodson, A survey of recent results in the spectral theory of ergodic dynamical systems, J. Dynam. Control Systems, 5 (1999), 173-226.
doi: 10.1023/A:1021726902801. |
[15] |
B. Hasselblatt and A. Katok, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511809187. |
[16] |
A. Katok, Bernoulli diffeomorphisms on surfaces, Ann. of Math. (2), 110 (1979), 529-547.
doi: 10.2307/1971237. |
[17] |
A. Katok, Combinatorical Constructions in Ergodic Theory and Dynamics, American Mathematical Society, Providence, RI, 2003.
doi: 10.1090/ulect/030. |
[18] |
J. Kwiatkowski and M. Lemańczyk, On the multiplicity function of ergodic group extensions. II, Studia Math., 116 (1995), 207-214. |
[19] |
A. Kriegl and P. Michor, The Convenient Setting of Global Analysis, American Mathematical Society, Providence, RI, 1997.
doi: 10.1090/surv/053. |
[20] |
A. Katok and A. Stepin, Approximations in ergodic theory, Russ. Math. Surveys, 22 (1967), 77-102.
doi: 10.1070/RM1967v022n05ABEH001227. |
[21] |
A. Katok and A. Stepin, Metric properties of measure preserving homeomorphisms, Russ. Math. Surveys, 25 (1970), 191-220.
doi: 10.1070/RM1970v025n02ABEH003793. |
[22] |
M. G. Nadkarni, Spectral Theory of Dynamical Systems, Birkhäuser Verlag, Basel, 1998.
doi: 10.1007/978-3-0348-8841-7. |
[23] |
H. Omori, Infinite Dimensional Lie Transformation Groups, Springer-Verlag, Berlin-New York, 1974. |
[24] |
V. I. Oseledets, An automorphism with simple continuous spectrum not having the group property, Mat. Zametki, 5 (1969), 323-326. |
[25] |
V. V. Ryzhikov, Transformations having homogeneous spectra, J. Dynam. Control Systems, 5 (1999), 145-148.
doi: 10.1023/A:1021748902318. |
[26] |
V. V. Ryzhikov, Homogeneous spectrum, disjointness of convolutions and mixing properties of dynamical systems, Selected Russian Math., 1 (1999), 13-24. |
[27] |
V. V. Ryzhikov, On the spectral and mixing properties of rank-1 constructions in ergodic theory, Doklady Mathematics, 74 (2006), 545-547. |
[28] |
A. M. Stepin, Properties of spectra of ergodic dynamical systems with locally compact time, Dokl. Akad. Nauk SSSR, 169 (1966), 773-776. |
[29] |
A. M. Stepin, Spectral properties of generic dynamical systems, Math. USSR Izv., 29 (1987), 159-192.
doi: 10.1070/IM1987v029n01ABEH000965. |
[1] |
Wen Huang, Zhiren Wang, Guohua Zhang. Möbius disjointness for topological models of ergodic systems with discrete spectrum. Journal of Modern Dynamics, 2019, 14: 277-290. doi: 10.3934/jmd.2019010 |
[2] |
Ryszard Rudnicki. An ergodic theory approach to chaos. Discrete and Continuous Dynamical Systems, 2015, 35 (2) : 757-770. doi: 10.3934/dcds.2015.35.757 |
[3] |
Thierry de la Rue. An introduction to joinings in ergodic theory. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 121-142. doi: 10.3934/dcds.2006.15.121 |
[4] |
Gary Froyland. On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 671-689. doi: 10.3934/dcds.2007.17.671 |
[5] |
Xiongping Dai, Yu Huang, Mingqing Xiao. Realization of joint spectral radius via Ergodic theory. Electronic Research Announcements, 2011, 18: 22-30. doi: 10.3934/era.2011.18.22 |
[6] |
Cristina Lizana, Vilton Pinheiro, Paulo Varandas. Contribution to the ergodic theory of robustly transitive maps. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 353-365. doi: 10.3934/dcds.2015.35.353 |
[7] |
Dmitry Kleinbock, Barak Weiss. Dirichlet's theorem on diophantine approximation and homogeneous flows. Journal of Modern Dynamics, 2008, 2 (1) : 43-62. doi: 10.3934/jmd.2008.2.43 |
[8] |
Maxim Sølund Kirsebom. Extreme value theory for random walks on homogeneous spaces. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4689-4717. doi: 10.3934/dcds.2014.34.4689 |
[9] |
Manfred Denker, Samuel Senti, Xuan Zhang. Fluctuations of ergodic sums on periodic orbits under specification. Discrete and Continuous Dynamical Systems, 2020, 40 (8) : 4665-4687. doi: 10.3934/dcds.2020197 |
[10] |
Hebai Chen, Jaume Llibre, Yilei Tang. Centers of discontinuous piecewise smooth quasi–homogeneous polynomial differential systems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6495-6509. doi: 10.3934/dcdsb.2019150 |
[11] |
Christoph Bandt, Helena PeÑa. Polynomial approximation of self-similar measures and the spectrum of the transfer operator. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 4611-4623. doi: 10.3934/dcds.2017198 |
[12] |
El Houcein El Abdalaoui, Joanna Kułaga-Przymus, Mariusz Lemańczyk, Thierry de la Rue. The Chowla and the Sarnak conjectures from ergodic theory point of view. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 2899-2944. doi: 10.3934/dcds.2017125 |
[13] |
Nimish Shah, Lei Yang. Equidistribution of curves in homogeneous spaces and Dirichlet's approximation theorem for matrices. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5247-5287. doi: 10.3934/dcds.2020227 |
[14] |
Xu Xu, Xin Zhao. Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model. Discrete and Continuous Dynamical Systems, 2020, 40 (8) : 4777-4800. doi: 10.3934/dcds.2020201 |
[15] |
Peng Huang, Xiong Li, Bin Liu. Invariant curves of smooth quasi-periodic mappings. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 131-154. doi: 10.3934/dcds.2018006 |
[16] |
Hajnal R. Tóth. Infinite Bernoulli convolutions with different probabilities. Discrete and Continuous Dynamical Systems, 2008, 21 (2) : 595-600. doi: 10.3934/dcds.2008.21.595 |
[17] |
Sergei A. Nazarov, Rafael Orive-Illera, María-Eugenia Pérez-Martínez. Asymptotic structure of the spectrum in a Dirichlet-strip with double periodic perforations. Networks and Heterogeneous Media, 2019, 14 (4) : 733-757. doi: 10.3934/nhm.2019029 |
[18] |
Juntao Sun, Jifeng Chu, Zhaosheng Feng. Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3807-3824. doi: 10.3934/dcds.2013.33.3807 |
[19] |
Fabien Durand, Alejandro Maass. A note on limit laws for minimal Cantor systems with infinite periodic spectrum. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 745-750. doi: 10.3934/dcds.2003.9.745 |
[20] |
Günter Leugering, Sergei A. Nazarov, Jari Taskinen. The band-gap structure of the spectrum in a periodic medium of masonry type. Networks and Heterogeneous Media, 2020, 15 (4) : 555-580. doi: 10.3934/nhm.2020014 |
2020 Impact Factor: 0.848
Tools
Metrics
Other articles
by authors
[Back to Top]