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For a function with 2 degrees of freedom, the 2-dimensional phase space that is accessible to the function or object is called its phase plane.

The partial differential equation u_(tt)-u_(xx)-u+u^3=0.

D_P(x)=lim_(epsilon->0)(lnmu(B_epsilon(x)))/(lnepsilon), where B_epsilon(x) is an n-dimensional ball of radius epsilon centered at x and mu is the probability measure.

A subset S subset R^n is said to be pseudo-convex at a point x in S if the associated pseudo-tangent cone P_S(x) to S at x contains S-{x}, i.e., if S-{x} subset P_S(x). Any ...

The pseudo-tangent cone P_S(x) of a subset S subset R^n at a point x in S is the set P_S(x)=convK_S^_, where K_S is the contingent cone of S and where conv(A) is the smallest ...

A function f defined on a subset S subset R^n is said to be pseudoconcave if -f is pseudoconvex.

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

The partial differential equation u_t+u_x-6uu_x-u_(txx)=0.

A method for predicting the onset of widespread chaos.

The Schwarzian derivative is defined by D_(Schwarzian)=(f^(''')(x))/(f^'(x))-3/2[(f^('')(x))/(f^'(x))]^2. The Feigenbaum constant is universal for one-dimensional maps if its ...