논문KCI 등재
C1-STABLY SHADOWABLE CONSERVATIVE DIFFEOMORPHISMS ARE ANOSOV
1
조회
0
다운로드
2
인용
0
참고문헌
키워드
주제분류수학
초록
In this short note we prove that if a symplectomorphism f is C1-stably shadowable, then f is Anosov. The same result is obtained for volume-preserving diffeomorphisms.
Abstract
In this short note we prove that if a symplectomorphism f is C1-stably shadowable, then f is Anosov. The same result is obtained for volume-preserving diffeomorphisms.
참고문헌 (14)
- "Hyperbolicity in the Volume Preserving Scenario"[URL]
- A. Arbieto, "A pasting lemma and some applications for conservative systems, With an appendix by David Diica and Yakov Simpson-Weller", Ergodic Theory Dynam. Systems, 27(5), pp.1399~1417 (2007)
- A. Avila, "On the regularization of conservative maps", Acta Math, 205(1), pp.5~18 (2010)
- M. Bessa, "A remark on the topological stability of symplectomorphisms", Appl. Math. Lett, 25(2), pp.163~165 (2012)
- C. Bonatti, "A C1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources", Ann. of Math, 158(2), pp.355~418 (2003)
- V. Horita, "Partial hyperbolicity for symplectic diffeomorphisms", Ann. Inst. H. Poincare Anal. Non Lineaire, 23(5), pp.641~661 (2006)
- K. Moriyasu, "The topological stability of diffeomorphisms", Nagoya Math. J, 123, pp.91~102 (1991)
- J. Moser, "On the volume elements on a manifold", Trans. Amer. Math. Soc, 120, pp.286~294 (1965)
- J. Moser, "Notes on dynamical systems, In Courant Lecture Notes in Mathematics, 12" (2005), American Mathematical Society
- S. Newhouse, "Quasi-eliptic periodic points in conservative dynamical systems", Amer. J. Math, 99(5), pp.1061~1087 (1977)
- S. Pilyugin, "Shadowing in Dynamical Systems, In Lecture Notes in Math., 1706", pp.1999~, Springer- Verlag
- K. Sakai, "C1-stably shadowable chain components", Ergodic Theory Dynam. Systems, 28(3), pp.987~1029 (2008)
- P. Walters, "On the pseudo-orbit tracing property and its relationship to stability, The structure of attractors in dynamical systems, In Lecture Notes in Math., 668", pp.231~244 (1978), Springer
- E. Zehnder, "Note on smoothing symplectic and volume-preserving diffeomorphisms, Ge- ometry and topology, In Lecture Notes in Math., Vol. 597", pp.828~854 (1977), Springer
이 간행물의 다른 논문 (27건)
The function analytic in the exterior of a disc and its application to periodic complex oscillationShi-an Gao, Zong-Xuan Chenpp. 1415-1432Morphic property of a quotient ring over polynomial ringQichuan Wang, Lianggui Feng, Kai Longpp. 1433-1439Note on the ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junctionZhongxue Lu, Zuhan Liupp. 1441-1450On some new theorems on multipliers in harmonic function spaces in higher dimension IIMilos Arsenovic, Romi F. Shamoyanpp. 1451-1469On entire solutions of nonlinear difference-differential equationsSongmin Wang, Sheng Lipp. 1471-1479
