^Camouzis, Elias; Ladas, G. (November 16, 2007). Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures. CRC Press. ISBN 9781584887669 – via Google Books.
^Kulenovic, Mustafa R. S.; Ladas, G. (July 30, 2001). Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures. CRC Press. ISBN 9781420035384 – via Google Books.
^Newth, Gerald, "World order from chaotic beginnings", Mathematical Gazette 88, March 2004, 39-45 gives a trigonometric approach.
and 29 Related for: Rational difference equation information
A rationaldifferenceequation is a nonlinear differenceequation of the form x n + 1 = α + ∑ i = 0 k β i x n − i A + ∑ i = 0 k B i x n − i , {\displaystyle...
of a differenceequation, the two terms "recurrence relation" and "differenceequation" are sometimes used interchangeably. See Rationaldifference equation...
Mandelbrot set Recurrence relation Matrix differenceequationRationaldifferenceequation Examples of differential equations Autonomous system (mathematics) Picard–Lindelöf...
A matrix differenceequation is a differenceequation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related...
inspection only works for quadratic equations that have rational roots. This means that the great majority of quadratic equations that arise in practical applications...
17 : ch. 10 (also known as a linear recurrence relation or linear differenceequation) sets equal to 0 a polynomial that is linear in the various iterates...
{1}{7}}} is a multivariate polynomial equation over the rational numbers. Some polynomial equations with rational coefficients have a solution that is...
The Antoine equation is a class of semi-empirical correlations describing the relation between vapor pressure and temperature for pure substances. The...
of the cubic equation do not necessarily belong to the same field as the coefficients. For example, some cubic equations with rational coefficients have...
when the degree of the equation decreases after having cleared the denominator). In the case of complex coefficients, a rational function with degree one...
algebraically closed field extension K of k, and make all equations true. When k is the field of rational numbers, K is generally assumed to be the field of...
theorem, and follows from the equation x 2 + y 2 = 1 {\displaystyle x^{2}+y^{2}=1} for the unit circle. This equation can be solved for either the sine...
root-finding algorithms. In practice, most algebraic equations of interest have integer or rational coefficients, and one may want a factorization with...
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example...
coefficients of the defining equation or equations of the curve are in K) and denote the curve by E. Then the K-rational points of E are the points on...
\alpha \in [0,1]} where n {\displaystyle n} is a rational number. "Theory of Fuzzy Differential Equations and Inclusions". Routledge & CRC Press. Retrieved...
matrix. The characteristic equation of a fourth-order linear differenceequation or differential equation is a quartic equation. An example arises in the...
areas are all rational numbers (positive rational solutions of the above equation) are sometimes also called Heronian triangles or rational triangles; in...
differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the...
are precisely the irrational solutions of quadratic equations with rational coefficients; rational solutions have finite continued fraction expansions...
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other...
mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems...
the second painlevé transcendent and the Korteweg-de Vries equation". Archive for Rational Mechanics and Analysis. 73 (1): 31–51. Bibcode:1980ArRMA..73...
the above equation. Many of the curves on Wikipedia's list of curves are rational and hence have similar rational parameterizations. Rational plane curves...
degree k. The rational function defined by the quotient of two homogeneous polynomials is a homogeneous function; its degree is the difference of the degrees...
differential equations and integral equations are functional equations. However, a more restricted meaning is often used, where a functional equation is an equation...
also studied the equations of some non-rational curves, for which no rational parametrisation is possible. He managed to find some rational points on these...
general linear equation in chapter eighteen of Brahmasphuṭasiddhānta, The difference between rupas, when inverted and divided by the difference of the [coefficients]...
numerator as a Fourier series. When a is a rational number, Hurwitz's formula leads to the following functional equation: For integers 1 ≤ m ≤ n {\displaystyle...
Global Information
