Tomoyuki Miyaji   Hisashi Okamoto   Alex D. D. Craik   
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 25(2) 2015年2月 [査読有り]
A three-dimensional autonomous dynamical system proposed by Pehlivan is untypical in simultaneously possessing both unbounded and chaotic solutions. Here, this topic is studied in some depth, both numerically and analytically. We find, by standard...
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES 90(10) 139-144 2014年12月 [査読有り]
We consider a three-dimensional dynamical system proposed in Physica D, 164, (2002), 168-186. It is a conservative system and is unusual in that most of the solutions are unbounded. The paper presented a conjecture that an unstable periodic orbit ...
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 31(3) 541-573 2014年11月 [査読有り]
We consider the generalized Proudman-Johnson equation with an external force. By varying the Reynolds number R and another nondimensional parameter a, branching stationary solutions are computed numerically for the global picture of bifurcations o...
We consider two-dimensional progressive water-waves, which propagate with a constant speed and a constant shape. Fluid motion is assumed to be irrotational. Trajectories in a coordinate system attached to the wave are easily computed by drawing co...