| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
The analogue of the Mandelbrot set in anti-holomorphic dynamics is called the tricorn. We prove that external rays and "umbilical cords" accumulating to the boundaries of hyperbolic components of odd period do not converge to a point. This non-landing property implies that the tricorn is much more complicated than the Mandelbrot set. Especially, the non-landingness of "umbilical cords" implies that the tricorn does not have such a self-similar property as for the Mandelbrot set.
We also construct a fundamental environment for visualization of Julia sets and bifurcation measures in complex two dimensional space with recent VR devices, so that we can easily implement various methods for controls, projections, rendering and so on for experiment.
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