| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
Constructing Lyapunov functions by verified numerics has been studied. It is well known that Lyapunov functions are very important tools in order to analyze dynamical systems. Once a Lyapunov function is constructed by verified numerics for a dynamical system, it can be used in mathematical proofs concerning the dynamical system. We have established the methods to construct Lyapunov functions with quadratic forms for continuous and discrete dynamical systems which have hyperbolic equilibria and fixed points, respectively. Our methods also verify areas included by the domain of the Lyapunov functions. Moreover we developed our method and investigated their applications and have obtained several interesting results.
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