2013 Fiscal Year Final Research Report
Analysis of non-hyperbolic systems through unstable periodic orbits
| Project/Area Number |
23740065
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hitotsubashi University (2013)
Hokkaido University (2011-2012) |
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Principal Investigator |
SAIKI Yoshitaka 一橋大学, 大学院商学研究科, 准教授 (20433740)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 力学系 / カオス / 不安定周期軌道 / リアプノフベクトル |
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| Research Abstract |
Dynamical systems can be classified into two types hyperbolic systems and non-hyperbolic systems. Hyperbolic systems have been understood well since the Smale's work. In this study we focus on non-hyperbolic systems and obtained some results in (1) strongly non-hyperbolic case, and (2) the occurrence of non-hyperbolicity by using unstable periodic orbits. Based on these results we have constructed cycle expansion theory which works well for the Henon map of a non-hyperbolic parameter.
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