| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We investigated the dynamics of polynomials and transcendental entire functions by mainly using complex analytic methods. As a remarkable result, we proved that the following phenomena which can be observed in the Mandelbrot set by computer graphics actually exist by formulating them mathematically and proving the statements: Take a small Mandelbrot set in the Mandelbrot set, and choose a parameter from it which corresponds to a quadratic polynomial with either a parabolic periodic point or whose critical point 0 is preperiodic. By zooming in its neighborhood, we can see a quasiconformal image of a Cantor Julia set which is a perturbation of a parabolic or Misiurewicz Julia set. Furthermore, by zooming in its middle part, we can see a certain nested structure ("decoration") and finally another "smaller Mandelbrot set" appears.
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