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The Lyapunov characteristic exponent [LCE] gives the rate of exponential divergence from perturbed initial conditions. To examine the behavior of an orbit around a point ...

Multivariable calculus is the branch of calculus that studies functions of more than one variable. Partial derivatives and multiple integrals are the generalizations of ...

Let f be a finite real-valued function defined on an interval [a,b]. Then at every point in [a,b] except on a set of Lebesgue measure zero, either: 1. There is a finite ...

A space D is connected if any two points in D can be connected by a curve lying wholly within D. A space is 0-connected (a.k.a. pathwise-connected) if every map from a ...

The conjecture that Frey's elliptic curve was not modular. The conjecture was quickly proved by Ribet (Ribet's theorem) in 1986, and was an important step in the proof of ...

A smooth curve is a curve which is a smooth function, where the word "curve" is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous ...

There are at least two maps known as the Hénon map. The first is the two-dimensional dissipative quadratic map given by the coupled equations x_(n+1) = 1-alphax_n^2+y_n (1) ...

A characterization of normal spaces which states that a topological space X is normal iff, for any two nonempty closed disjoint subsets A, and B of X, there is a continuous ...

A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

Let f:A->B be a map between sets A and B. Let Y subset= B. Then the preimage of Y under f is denoted by f^(-1)(Y), and is the set of all elements of A that map to elements in ...