-
Previous Article
Sharp regularity for degenerate obstacle type problems: A geometric approach
- DCDS Home
- This Issue
-
Next Article
Entropy production in random billiards
Gromov-Hausdorff stability for group actions
1. | Department of Mathematics, College of Science, Yanbian University, No. 977, Gongyuan Road, Yanji City 133002, Jilin Province, China |
2. | Department of Mathematics, Chungnam National University, Daejeon 305-764, Korea |
3. | Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530 21945-970, Rio de Janeiro, Brazil |
We will extend the topological Gromov-Hausdorff stability [
References:
[1] |
D. V. Anosov,
Roughness of geodesic flows on compact Riemannian manifolds of negative curvature, Dokl. Akad. Nauk SSSR, 145 (1962), 707-709.
|
[2] |
A. Arbieto and C. A. Morales Rojas,
Topological stability from Gromov-Hausdorff viewpoint, Discrete Contin. Dyn. Syst., 37 (2017), 3531-3544.
doi: 10.3934/dcds.2017151. |
[3] |
D. Burago, Y. Burago and S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics, 33, American Mathematical Society, Providence, RI, 2001.
doi: 10.1090/gsm/033. |
[4] |
N.-P. Chung and K. Lee,
Topological stability and pseudo-orbit tracing property of group actions, Proc. Amer. Math. Soc., 146 (2018), 1047-1057.
doi: 10.1090/proc/13654. |
[5] |
M. Dong, Group Actions from Measure Theoretical Viewpoint, PhD. thesis, Chungnam National University in Daejeon, 2018. |
[6] |
K. Fukaya,
Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Invent. Math., 87 (1987), 517-547.
doi: 10.1007/BF01389241. |
[7] |
M. Gromov,
Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math., 53 (1981), 53-73.
|
[8] |
A. M. Lyapunov,
The general problem of the stability of motion, Internat. J. Control, 55 (1992), 521-790.
doi: 10.1080/00207179208934253. |
[9] |
A. V. Osipov and S. B. Tikhomirov,
Shadowing for actions of some finitely generated groups, Dyn. Syst., 29 (2014), 337-351.
doi: 10.1080/14689367.2014.902037. |
[10] |
S. Y. Pilyugin and S. B. Tikhomirov,
Shadowing in actions of some Abelian groups, Fund. Math., 179 (2003), 83-96.
doi: 10.4064/fm179-1-7. |
[11] |
P. Walters, On the pseudo-orbit tracing property and its relationship to stability, in The Structure of Attractors in Dynamical Systems, Lecture Notes in Math., 668, Springer, Berlin, 1978,231–244.
doi: 10.1007/BFb0101795. |
show all references
References:
[1] |
D. V. Anosov,
Roughness of geodesic flows on compact Riemannian manifolds of negative curvature, Dokl. Akad. Nauk SSSR, 145 (1962), 707-709.
|
[2] |
A. Arbieto and C. A. Morales Rojas,
Topological stability from Gromov-Hausdorff viewpoint, Discrete Contin. Dyn. Syst., 37 (2017), 3531-3544.
doi: 10.3934/dcds.2017151. |
[3] |
D. Burago, Y. Burago and S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics, 33, American Mathematical Society, Providence, RI, 2001.
doi: 10.1090/gsm/033. |
[4] |
N.-P. Chung and K. Lee,
Topological stability and pseudo-orbit tracing property of group actions, Proc. Amer. Math. Soc., 146 (2018), 1047-1057.
doi: 10.1090/proc/13654. |
[5] |
M. Dong, Group Actions from Measure Theoretical Viewpoint, PhD. thesis, Chungnam National University in Daejeon, 2018. |
[6] |
K. Fukaya,
Collapsing of Riemannian manifolds and eigenvalues of Laplace operator, Invent. Math., 87 (1987), 517-547.
doi: 10.1007/BF01389241. |
[7] |
M. Gromov,
Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math., 53 (1981), 53-73.
|
[8] |
A. M. Lyapunov,
The general problem of the stability of motion, Internat. J. Control, 55 (1992), 521-790.
doi: 10.1080/00207179208934253. |
[9] |
A. V. Osipov and S. B. Tikhomirov,
Shadowing for actions of some finitely generated groups, Dyn. Syst., 29 (2014), 337-351.
doi: 10.1080/14689367.2014.902037. |
[10] |
S. Y. Pilyugin and S. B. Tikhomirov,
Shadowing in actions of some Abelian groups, Fund. Math., 179 (2003), 83-96.
doi: 10.4064/fm179-1-7. |
[11] |
P. Walters, On the pseudo-orbit tracing property and its relationship to stability, in The Structure of Attractors in Dynamical Systems, Lecture Notes in Math., 668, Springer, Berlin, 1978,231–244.
doi: 10.1007/BFb0101795. |
[1] |
Samir Chowdhury, Facundo Mémoli. Explicit geodesics in Gromov-Hausdorff space. Electronic Research Announcements, 2018, 25: 48-59. doi: 10.3934/era.2018.25.006 |
[2] |
Nhan-Phu Chung. Gromov-Hausdorff distances for dynamical systems. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 6179-6200. doi: 10.3934/dcds.2020275 |
[3] |
Alexanger Arbieto, Carlos Arnoldo Morales Rojas. Topological stability from Gromov-Hausdorff viewpoint. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3531-3544. doi: 10.3934/dcds.2017151 |
[4] |
Jihoon Lee, Nguyen Thanh Nguyen. Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1263-1296. doi: 10.3934/cpaa.2021020 |
[5] |
Brandon Seward. Every action of a nonamenable group is the factor of a small action. Journal of Modern Dynamics, 2014, 8 (2) : 251-270. doi: 10.3934/jmd.2014.8.251 |
[6] |
Soonki Hong, Seonhee Lim. Martin boundary of brownian motion on Gromov hyperbolic metric graphs. Discrete and Continuous Dynamical Systems, 2021, 41 (8) : 3725-3757. doi: 10.3934/dcds.2021014 |
[7] |
Jaeyoo Choy, Hahng-Yun Chu. On the dynamics of flows on compact metric spaces. Communications on Pure and Applied Analysis, 2010, 9 (1) : 103-108. doi: 10.3934/cpaa.2010.9.103 |
[8] |
S. A. Krat. On pairs of metrics invariant under a cocompact action of a group. Electronic Research Announcements, 2001, 7: 79-86. |
[9] |
Joseph Auslander, Xiongping Dai. Minimality, distality and equicontinuity for semigroup actions on compact Hausdorff spaces. Discrete and Continuous Dynamical Systems, 2019, 39 (8) : 4647-4711. doi: 10.3934/dcds.2019190 |
[10] |
Feimin Zhong, Jinxing Xie, Jing Jiao. Solutions for bargaining games with incomplete information: General type space and action space. Journal of Industrial and Management Optimization, 2018, 14 (3) : 953-966. doi: 10.3934/jimo.2017084 |
[11] |
Xiaojun Huang, Yuan Lian, Changrong Zhu. A Billingsley-type theorem for the pressure of an action of an amenable group. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 959-993. doi: 10.3934/dcds.2019040 |
[12] |
Carlos Matheus, Jean-Christophe Yoccoz. The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis. Journal of Modern Dynamics, 2010, 4 (3) : 453-486. doi: 10.3934/jmd.2010.4.453 |
[13] |
Bertuel Tangue Ndawa. Infinite lifting of an action of symplectomorphism group on the set of bi-Lagrangian structures. Journal of Geometric Mechanics, 2022 doi: 10.3934/jgm.2022006 |
[14] |
Evgeny L. Korotyaev. Estimates for solutions of KDV on the phase space of periodic distributions in terms of action variables. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 219-225. doi: 10.3934/dcds.2011.30.219 |
[15] |
Jordi Gaset, Narciso Román-Roy. New multisymplectic approach to the Metric-Affine (Einstein-Palatini) action for gravity. Journal of Geometric Mechanics, 2019, 11 (3) : 361-396. doi: 10.3934/jgm.2019019 |
[16] |
Martin Pinsonnault. Maximal compact tori in the Hamiltonian group of 4-dimensional symplectic manifolds. Journal of Modern Dynamics, 2008, 2 (3) : 431-455. doi: 10.3934/jmd.2008.2.431 |
[17] |
Michael Field, Ian Melbourne, Matthew Nicol, Andrei Török. Statistical properties of compact group extensions of hyperbolic flows and their time one maps. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 79-96. doi: 10.3934/dcds.2005.12.79 |
[18] |
Anton Stolbunov. Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Advances in Mathematics of Communications, 2010, 4 (2) : 215-235. doi: 10.3934/amc.2010.4.215 |
[19] |
Qinian Jin, YanYan Li. Starshaped compact hypersurfaces with prescribed $k$-th mean curvature in hyperbolic space. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 367-377. doi: 10.3934/dcds.2006.15.367 |
[20] |
Paolo Perfetti. Fixed point theorems in the Arnol'd model about instability of the action-variables in phase-space. Discrete and Continuous Dynamical Systems, 1998, 4 (2) : 379-391. doi: 10.3934/dcds.1998.4.379 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]