書誌事項
- 公開日
- 2014-03-14
- 資源種別
- journal article
- 権利情報
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- https://www.cambridge.org/core/terms
- DOI
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- 10.1017/etds.2013.105
- 10.48550/arxiv.1212.1634
- 公開者
- Cambridge University Press (CUP)
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説明
<jats:p>We define the notion of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385713001053_inline1" /><jats:tex-math>${\it\varepsilon}$</jats:tex-math></jats:alternatives></jats:inline-formula>-flexible periodic point: it is a periodic point with stable index equal to two whose dynamics restricted to the stable direction admits <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385713001053_inline2" /><jats:tex-math>${\it\varepsilon}$</jats:tex-math></jats:alternatives></jats:inline-formula>-perturbations both to a homothety and a saddle having an eigenvalue equal to one. We show that an <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385713001053_inline3" /><jats:tex-math>${\it\varepsilon}$</jats:tex-math></jats:alternatives></jats:inline-formula>-perturbation to an <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385713001053_inline4" /><jats:tex-math>${\it\varepsilon}$</jats:tex-math></jats:alternatives></jats:inline-formula>-flexible point allows us to change it to a stable index one periodic point whose (one-dimensional) stable manifold is an arbitrarily chosen <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385713001053_inline5" /><jats:tex-math>$C^{1}$</jats:tex-math></jats:alternatives></jats:inline-formula>-curve. We also show that the existence of flexible points is a general phenomenon among systems with a robustly non-hyperbolic two-dimensional center-stable bundle.</jats:p>
収録刊行物
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- Ergodic Theory and Dynamical Systems
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Ergodic Theory and Dynamical Systems 35 (5), 1394-1422, 2014-03-14
Cambridge University Press (CUP)
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詳細情報 詳細情報について
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- CRID
- 1360004233000809984
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- ISSN
- 14694417
- 01433857
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- 資料種別
- journal article
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- データソース種別
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