TITLE
	Formation of fractal structure in many-body systems with attractive power-law potentials	

AUTHOR
	Hiroko KOYAMA

ABSTRACT 
	Formation of spatial structures, which is seen over a wide range of areas, 
	from protein folding in biological systems to large-scale structures of the 
	Universe, is a most interesting phenomenon in nature. Theoretical origins of 
	such structure are quite important and will be classified into several cases. 
	One of the most interesting classes as a subject of dynamical systems is 
	that some remarkable structure and organization is created dynamically by 
	the mutual interaction among the elements. We have shown that spatial 
	structure with fractal distribution emerges spontaneously from uniformly 
	random initial conditions in 1-dimensional self-gravitating system. The 
	structures created in small spatial scale grow up to larger scale through 
	clustering of clusters, and form power-law correlation. The power-law 
	structure persists even after the system is virialized, and gradually 
	disappears owing to energy exchange among particles. Energy distribution is 
	quasi-stationary after the system is virialized. Recently, we have studied 
	the formation of fractal structure in 1-dimensional many-body systems with 
	attractive power-law potentials. The numerical analysis has clarified that 
	the range of the index of the power for which fractal structure emerges is 
	limited. In this presentation we report above results and discuss about the 
	dynamical mechanism underlying pattern formation in Hamiltonian systems.