| Project/Area Number |
18540187
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Kumamoto University |
|---|
Principal Investigator |
NAITO Koichiro Kumamoto University, Grad. Sch. Sci. Tech., Prof. (10164104)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
OSHIMA Yoichi Kumamoto Univ., Grad. Sch. Sci. Tech., Prof. (20040404)
MISAWA Masashi Kumamoto Univ., Grad. Sch. Sci. Tech., Prof. (40242672)
KADOTA Noriya Kumamoto Univ., Grad. Sch. Sci. Tech., Lect. (80185884)
|
|---|
| Project Period (FY) |
2006 – 2007
|
| Project Status |
Completed (Fiscal Year 2007)
|
| Budget Amount *help |
¥3,880,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥480,000)
Fiscal Year 2007: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2006: ¥1,800,000 (Direct Cost: ¥1,800,000)
|
|---|
| Keywords | nonlinear PDE / quasi periodicity / attractor / fractal dimension / Diophantine approximation / KAM theorem / self-similarity / chaos |
|---|
| Research Abstract |
In our previous research, classifying irrational numbers according to the orders of goodness or badness levels of approximation by rational numbers, we introduced the parameterized Diophantine condition, we say d_0- (D) condition, and we also proposed the gaps between the upper and the lower recurrent dimensions as the index parameters, which measure unpredictability levels of the orbits.
In this research, using these orders of the d_0-(D) conditions, we estimate the gaps of recurrent dimensions of quasi-periodic orbits given by the circle mappings or the Gauss map. These results were announced by the head investigator in the COE conference (Keio University) and in Yokohama Math.J. ([3]) and in J. Nonlinear and Convex Analysis ([4]).
To analyze complexity of quasi-periodic solutions given by various types of partial differential equations we estimate the recurrent dimensions by using the d_0- (D) conditions for their irrational frequencies of these solutions. The head investigator announced these results in Taiwan. J. Math. ([1]) and in Proc.4th Conf.on NACA ([5]) and the co-investigator M. Misawa in [6] has shown some related results on nonlin-ear P.D.E., which are important and essential to investigate chaotic behaviors of nonlinear dynamical systems. In [7] the co-investigator Y. Oshima also proved some related results for randomness, using probability theory.
|
