Dynamical difference equations

Difference Equations as Discrete Dynamical Systems

Lia Vas Discrete Dynamical Systems . Difference Equations

If values that we monitor changes during discrete periods (for example, in discrete time intervals), the formula above leads to a difference equation or a dynamical system. In this case, we are dealing with a function that depends on discrete integer values – a sequence. Recall that a sequence of real numbers (indexed by nonnegative integers) can be given by listing its terms (for example, 1, 1...

Skew-product dynamical systems: Applications to difference equations

One of the earliest difference equations, the Fibonacci sequence, was introduced in 1202 in “Liberabaci,” a book about the abacus, by the famous Italian Leonardo di Pisa, better known as Fibonacci. The problem may be stated as follows: how many pairs of rabbits will there be after one year when starting with one pair of mature rabbits, if each pair of rabbits give birth to a new pair each month...

Skew-Product Dynamical Dystems: Applications to Difference Equations

‘degeneration of Trigonometric Dynamical Difference Equations for Quantum Loop Algebras to Trigonometric Casimir Equations for Yangians’

We show that, under Drinfeld’s degeneration [D] of quantum loop algebras to Yangians, the trigonometric dynamical difference equations [EV] for the quantum affine algebra degenerate to the trigonometric Casimir differential equations [TL] for Yangians.