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Li and Yorke (1975) proved that any one-dimensional system which exhibits a regular cycle of period three will also display regular cycles of every other length as well as ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

A function f(x) is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period p if f(x)=f(x+np) for ...

A square matrix A such that the matrix power A^(k+1)=A for k a positive integer is called a periodic matrix. If k is the least such integer, then the matrix is said to have ...

A point x_0 is said to be a periodic point of a function f of period n if f^n(x_0)=x_0, where f^0(x)=x and f^n(x) is defined recursively by f^n(x)=f(f^(n-1)(x)).

A sequence {a_i} is said to be periodic with period p with if it satisfies a_i=a_(i+np) for n=1, 2, .... For example, {1,2,1,2,1,2,1,2,1,2,1,2,1,2,...} is a periodic sequence ...

F(x,s) = sum_(m=1)^(infty)(e^(2piimx))/(m^s) (1) = psi_s(e^(2piix)), (2) where psi_s(x) is the polygamma function.

A graphical plot with abscissa given by the number p of consecutive numbers constituting a single period and ordinate given by the correlation ratio eta. The equation of the ...

A node in a graph for which the graph eccentricity equals the graph diameter (Harary 1994, p. 41).

The Perkel graph is a weakly regular graph on 57 vertices and 171 edges, shown above in several embeddings. It is the unique distance-regular graph with intersection array ...