15 citations · 103 across the 32 of their papers we have counts for
32 papers
Big Crunch on Julia and Anti-Julia Sets in the Integrable Limit
Masatomi Iizawa, Satoru Saito, Yasuhito Narita +3
The Julia set is defined by the closure of repelling periodic points in chaotic systems. Why does this structure not appear in integrable systems? In this paper, we address this qu…
Dynamic Logic of Quantum Field Theory
Tsubasa Takagi, Hiroki Hoshina, Masatomi Iizawa +1
Although logic of quantum mechanics has been studied for a long time, logic of QFT has not been studied before. We formulate logic of QFT by introducing the perspective of dynamic…
Singularity Confinement and Projective Resolution of Triangulated Category
Satoru Saito, Tsukasa Yumibayashi, Yuki Wakimoto
We proposed, in our previous paper, to characterize the Hirota-Miwa equation by means of the theory of triangulated category. We extend our argument in this paper to support the id…
Degeneration of the Julia set to singular loci of algebraic curves
Satoru Saito, Noriko Saitoh, Hiromitsu Harada +2
We show that, when a non-integrable rational map changes to an integrable one continuously, a large part of the Julia set of the map approach indeterminate points (IDP) of the map…
Derivation of Invariant Varieties of Periodic Points from Singularity Confinement in the case of Toda Map
Tsukasa Yumibayashi, Satoru Saito, Yuki Wakimoto
In our previous work we have shown that the invariant varieties of periodic points (IVPP) of all periods of the 3 dimensional Lotka-Volterra map can be derived, iteratively, from t…
On recurrence equations associated with invariant varieties of periodic points
Satoru Saito, Noriko Saitoh
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived f…