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The circle map is a one-dimensional map which maps a circle onto itself theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n), (1) where theta_(n+1) is computed mod 1 and K is a ...

The Feigenbaum constant delta is a universal constant for functions approaching chaos via period doubling. It was discovered by Feigenbaum in 1975 (Feigenbaum 1979) while ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

A plot of the map winding number W resulting from mode locking as a function of Omega for the circle map theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n) (1) with K=1. (Since ...

A theorem outlined by Kolmogorov (1954) which was subsequently proved in the 1960s by Arnol'd (1963) and Moser (1962; Tabor 1989, p. 105). It gives conditions under which ...

The parameter r (sometimes also denoted mu) in the logistic equation x_(n+1)=rx_n(1-x_n).

An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...

Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

Mathematical growth in which one population grows at a rate proportional to the power of another population.