논문KCI 등재
Singular hyperbolicity of $C^1$ generic three dimensional vector fields
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In the paper, we show that for a generic $C^1$ vector field $X$ on a closed three dimensional manifold $M$, any isolated transitive set of $X$ is singular hyperbolic. It is a partial answer of the conjecture in \cite{MP}.
Abstract
In the paper, we show that for a generic $C^1$ vector field $X$ on a closed three dimensional manifold $M$, any isolated transitive set of $X$ is singular hyperbolic. It is a partial answer of the conjecture in \cite{MP}.
참고문헌 (19)
- F. Abdenur, "Global dominated splittings and the C1 Newhouse phenomenon", Proc. Amer. Math. Soc, 134(8), pp.2229~2237 (2006)[DOI]
- C. Bonatti, "Persistent nonhyperbolic transitive diffeomorphisms", Ann. of Math, 143(2), pp.357~396 (1996)[DOI]
- 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)[DOI]
- C. M. Carballo, "Maximal transitive sets with singularities for generic C1 vector fields", Bol. Soc. Brasil. Mat. (N. S.), 31(3), pp.287~303 (2000)[DOI]
- L. J. Dıaz, "Partial hyperbolicity and robust transitivity", Acta Math, 183(1), pp.1~43 (1999)[DOI]
- J. Guckenheimer, "The Hopf Bifurcation Theorem and its Applications" (1976), Springer-Verlag
- M. Li, "Robustly transitive singular sets via approach of an extended linear Poincar´e flow", Discrete Contin. Dyn. Syst, 13(2), pp.239~269 (2005)[DOI]
- S. T. Liao, "Obstruction sets I", Acta Math. Sinica, 23(3), pp.411~453 (1980)
- S. T. Liao, "Obstruction sets II", Acta Sci. Natur. Univ. Pekinensis, 2, pp.1~36 (1981)
- E. N. Lorenz, "Deterministic nonperiodic flow", J. Atmospheric Sci, 20(2), pp.130~141 (1963)
- R. Mane, "An ergodic closing lemma", Ann. of Math, 116(3), pp.503~540 (1982)[DOI]
- R. Mane, "A proof of the C1 stability conjecture", Publ. Math. IHES, 66, pp.161~210 (1988)
- C. A. Morales, "A dichotomy for three-dimensional vector fields", Ergod. Th. & Dynam. Syst, 23, pp.1575~1600 (2003)
- C. A. Morales, "Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers", Ann. of Math, 160(2), pp.375~432 (2004)[DOI]
- J. Palis Jr., "Geometric theory of dynamical systems, translated from the Portuguese by A. K. Manning" (1982), Springer
- Y. Shi, "On the singular-hyperbolicity of star flows", J. Mod. Dyn, 8(2), pp.191~219 (2014)[DOI]
- L. Wen, "On the C1 stability conjecture for flows", J. Differential Equations, 129(2), pp.334~357 (1996)[DOI]
- L. Wen, "Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles", Bull. Braz. Math. Soc. (N. S.), 35(3), pp.419~452 (2004)[DOI]
- X. Wen, "A characterization of singular hyperbolicity via the linear Poincar´e flow", J. Differential Equations, 268(8), pp.4256~4275 (2020)[DOI]
관련 논문AI추천
Generic diffeomorphisms with robustly transitive sets이건희, 이만섭, 이승희대한수학회 · 대한수학회논문집2013 · 제28권 제3호The local star condition for generic transitive diffeomorphismsManseob Lee대한수학회 · 대한수학회논문집2016 · 제31권 제2호Continuum-wise expansiveness for $C^1$ generic vector fields이만섭대한수학회 · 대한수학회지2023 · 제60권 제5호LIMIT WEAK SHADOWABLE TRANSITIVE SETS OF C¹-GENERIC DIFFEOMORPHISMS이만섭, Gang Lu대한수학회 · 대한수학회논문집2012 · 제27권 제3호ON C1-GENERIC HYPERBOLICITY OF HOMOCLINIC CLASSES강보원, 이만섭, N. Koo장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제3호Hyperbolicity of chain transitive sets with limit shadowing이승희, Abbas Fakhari, Khosro Tajbakhsh대한수학회 · 대한수학회보2014 · 제51권 제5호
이 간행물의 다른 논문 (8건)
Self-pair homotopy equivalences related to co-variant functors이기영, 신혜선, 최호원pp. 409-425Smooth singular value thresholding algorithm for low-rank matrix completion problem이근섭pp. 427-444Properties of positive solutions for the fractional Laplacian systems with positive-negative mixed powersMengjia Niu, Anjie Yuan, Yuanyuan Shen, Zhongxue Lupp. 445-459Continuity of the maximal commutators in Sobolev spacesXixi Jiang, Feng Liupp. 461-494Reduction of abelian varieties and curvesMoshe Jarden, Aharon Razonpp. 515-545