| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
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| Outline of Final Research Achievements |
On the C1 Palis Conjecture saying that in the complement of the closure of C1 diffeomorphisms having the uniform hyperbolicity (Axiom A + no cycle condition) there exist a dense subset of those exhibiting homoclinic bifurcations, we prove that the conjecture is true if C2 ergodic measures with zero Lyapunov exponents are destroyed by C1 small perturbations. For the 2-dimensional case, if Smale Conjecture saying that uniformly hyperbolic diffeomorphisms are dense in C1 surface diffeomorphisms is not true, then (taking the inverse if necessary) in a residual subset of the complement of uniformly hyperbolic diffeomorphisms, there exist infinitely many sinks, which are either observable or pathological. Moreover, we developed a new C1 closing lemma for C2 diffeomorphisms under some condition.
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