Ultradiscretization of solvable one-dimensional chaotic maps

Kajiwara, Kenji; Nobe, Atsushi; Tsuda, Teruhisa

doi:10.1088/1751-8113/41/39/395202

Cited by 8 publications

(16 citation statements)

References 38 publications

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“…There are various levels of discreteness, for example, difference equation, coupled map lattice, cellular automaton (CA), and so on. Among them, max-plus equation is quite novel expression and studied intensively in recent years [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Max-plus equation with two conserved quantities and one monotonically decreasing quantity

Tokieda

Takahashi

2018

JSIAM Letters

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We propose a max-plus equation as an extension of 1+1D cellular automaton of four neighbors. It has two conserved quantities and one monotonically decreasing quantity which are max-plus analogues of those of the binary cellular automaton. It is interesting that one of the quantities is global and defined by the maximum value of dependent variable. We show proofs about their conservation and monotonicity using max-plus formulas.

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Section: Introductionmentioning

confidence: 99%

Max-plus equation with two conserved quantities and one monotonically decreasing quantity

Tokieda

Takahashi

2018

JSIAM Letters

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“…For example, they appear when the equation of motion of the bead on a rotating hoop is solved, 37 or in the study of the nonlinear Schrodinger equation in the context of Bose-Einstein condensates, 38 or when population growth dynamics is studied, 39 as well as in other fields of physics. [40][41][42][43]…”

Section: Introductionmentioning

confidence: 99%

A Jacobian generalization of the pseudo-Nambu–Goldstone boson potential

Hipólito-Ricaldi

Villanueva

2017

Int. J. Mod. Phys. D

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We enlarge the classes of inflaton and quintessence fields by generalizing the pseudo Nambu-Goldstone boson potential by means of elliptic Jacobian functions, which are characterized by a parameter k. We use such a generalization to implement an inflationary era and a late acceleration of the universe. As an inflationary model the Jacobian generalization leads us to a number of e-foldings and a primordial spectrum of perturbations compatible with the Planck collaboration 2015. As a quintessence model, a study of the evolution of its equation of state (EoS) and its w ′ -w plane helps us to classify it as a thawing model. This allows us to consider analytical approximations for the EoS recently discovered for thawing quintessence. By using JLA Supernovae Ia and Hubble parameter H(z) data sets, we perform an observational analysis of the viability of the model as quintessence.

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“…. on E λ so called the solvable chaotic system [17,19,8,7]. This dynamical system behaves chaotically, nevertheless we can construct its general solution by using the level-three theta functions as in the case of the QRT system [8,7].…”

Section: Introductionmentioning

confidence: 99%

Group actions on the tropical Hesse pencil

Nobe

2016

Japan J. Indust. Appl. Math.

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We show that the addition of points on the tropical Hesse curve can be realized via the intersection with a tropical line. Then the addition formula for the tropical Hesse curve is reduced from those for the level-three theta functions through the ultradiscretization procedure. A tropical analogue of the Hessian group G 216 , the group of linear automorphisms acting on the Hesse pencil, is also investigated; it is shown that the dihedral group D 3 of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.

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Ultradiscretization of solvable one-dimensional chaotic maps

Cited by 8 publications

References 38 publications

Max-plus equation with two conserved quantities and one monotonically decreasing quantity

Max-plus equation with two conserved quantities and one monotonically decreasing quantity

A Jacobian generalization of the pseudo-Nambu–Goldstone boson potential

Group actions on the tropical Hesse pencil

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