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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
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Let $f:M{\rightarrow}M$ be a diffeomorphism of a compact smooth manifold M. In this paper, we show that $C^1$ generically, if a chain transitive set ${\Lambda}$ is locally maximal then it admits a dominated splitting. Moreover, $C^1$ generically if a chain transitive set ${\Lambda}$ of f is locally maximal then it has zero entropy.
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참고문헌 (15)
참고문헌 신청
F. Abdenur / 2006 / Global dominated splitting and the C1Newhouse phenomenon / Proc. Amer. Math. Soc 134:2229~2237
F. Abdenur / 2011 / Nonuniform hyperbolicity for generic diffeomorphisms / Israel J. Math 183:1~60
C. Bonatti / 2003 / A C1-generic dichotomy for diffeomor-phisms: weak forms of hyperbolicity or in nitely many sinks or sources / Ann. of Math 158(2):355~418
S. Crovisier / 2006 / Periodic orbits and chain transitive sets of C1 diffeomorphisms / Math. de L'ihe's 104:87~141
K. Lee / 2012 / Stably inverse shadowable transitive sets and dominated splitting / Proc. Amer. Math. Soc 140(1):217~226
F. Abdenur / 2011 / Nonuniform hyperbolicity for generic diffeomorphisms / Israel J. Math 183:1~60
C. Bonatti / 2003 / A C1-generic dichotomy for diffeomor-phisms: weak forms of hyperbolicity or in nitely many sinks or sources / Ann. of Math 158(2):355~418
S. Crovisier / 2006 / Periodic orbits and chain transitive sets of C1 diffeomorphisms / Math. de L'ihe's 104:87~141
K. Lee / 2012 / Stably inverse shadowable transitive sets and dominated splitting / Proc. Amer. Math. Soc 140(1):217~226
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