Consider the two-dimensional area-preserving map which satisfies the condition that the Smale horseshoe exists at a ≥ a_c > 0. In the horseshoe, every periodic orbit is uniquely coded by two symbols 0 and 1. As a result, the symbol sequence s represented by 0 and 1 is determined. For the periodic orbit, the symbol sequence s is the repetition of a finite number of symbols named the code. Suppose that the mother periodic orbit M undergoes the period-doubling bifurcation. Then, the first generation of daughter periodic orbit D₁ appears from M. The n (≥ 1)-th generation of daughter periodic orbit D_n is also defined. Let P₀ be the code for M and P_n be the code for D_n (n ≥ 1). Our purpose is to derive the coding rule to determine P_n from the given P₀. The coding rules for the restricted symmetric periodic orbits are derived.

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Astronomy Data Center constructs a system to analyze a huge data set, such as large-scale survey data obtained by wide-field cameras including Hyper Suprime-Cam at the Subaru Telescope, that require much computing resources for processing, and operates the system in collaboration with the Subaru Telescope since September 2019.
The system consists of a login node, a management node, 35 compute nodes, a storage with 5 PB capacity and high speed I/O, and file servers with redundant configuration. All nodes other than the management node are connected by InfiniBand with bandwidth of 56 Gbps or more. Computing resources of the system are managed by a job scheduler. Interactive use of compute nodes are prohibited.
Although the computing resources at the start of operation were 280 CPU cores and 5 TB memory, the significant addition of compute nodes in spring 2020 expands the total resources to 1,976 cores and 18.5 TB memory. The additional nodes are currently used for the analysis of HSC-SSP that also serves as trial operation. After adjusting of queue settings, the nodes are to be shortly released for HSC open-use observers.
The performance evaluation tests, conducted before the start of operation, reveal that the speed of reading and writing files is 24–26 GB s⁻¹, and that the processing speed of HSC data is four times faster than that on the batch servers of Multi-Wavelength Data Analysis System.

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