In mathematics, the Hopf decomposition, named after Eberhard Hopf, gives a canonical decomposition of a measure space (X, μ) with respect to an invertible...

Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as a method...

of wandering sets. The Hopf decomposition states that every measure space with a non-singular transformation can be decomposed into an invariant conservative...

1-parameter group of automorphisms σt of A = L∞(X,μ), then by the Hopf decomposition either every St with t ≠ 0 is dissipative or every St with t ≠ 0 is...

Eberhard Frederich Ferdinand Hopf (April 4, 1902 in Salzburg, Austria-Hungary – July 24, 1983 in Bloomington, Indiana, USA) was a German mathematician...

the robustness of biological systems. The Hopf decomposition states that dynamical systems can be decomposed into a conservative and a dissipative part;...

systolic geometry. Techniques include the study of ergodic flows, the Hopf decomposition, and the Ambrose–Kakutani–Krengel–Kubo theorem. An important class...

In mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component. It consists of two circles linked together exactly...

This is called a pants decomposition for the surface, and the curves are called the cuffs of the decomposition. This decomposition is not unique, but by...

that the Hodge decomposition is a decomposition of cohomology with complex coefficients that usually does not come from a decomposition of cohomology with...

set of measure zero. The Hopf decomposition states that every measure space with a non-singular transformation can be decomposed into an invariant conservative...

Dirichlet boundary condition Neumann boundary condition Stefan problem Wiener–Hopf problem Separation of variables Green's function Elliptic partial differential...

perhaps best known today for his result on the existence of the Schur decomposition and for his work on group representations (Schur's lemma). Schur published...

structure is known as the Hopf problem, after Heinz Hopf. Just as a complex structure on a vector space V allows a decomposition of VC into V+ and V− (the...

numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes. After the proof of the simplicial...

Gauss decomposition is a generalization of the LU decomposition for the general linear group and a specialization of the Bruhat decomposition. For GL(V)...

also follows from the work of Smale about handle decompositions from Morse theory. The decomposition of M into two handlebodies is called a Heegaard splitting...

These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital...

example: The unknot, trefoil knot, and figure-eight knot are fibered knots. The Hopf link is a fibered link. The Alexander polynomial of a fibered knot is monic...

4D rotations, an even more useful coordinate system for 4D is provided by Hopf coordinates {ξ1, η, ξ2}, which are a set of three angular coordinates specifying...

so they comprise a complete Hopf fibration; there is no room for more 150-cell tori of this kind. To get a decomposition of the 600-cell into four 150-cell...

is the dual vector space. The Hopf algebras associated to groups have a commutative algebra structure, and so general Hopf algebras are known as quantum...

giving the 3-sphere the structure of a principal circle bundle known as the Hopf bundle. If one thinks of S3 as a subset of C2, the action is given by ( z...

Torus Unknot (01) Trefoil (31) Cinquefoil (51) Septafoil (71) Unlink (02 1) Hopf (22 1) Solomon's (42 1) Invariants Alternating Arf invariant Bridge no. 2-bridge...

i > n. The first such surprise was the discovery of a mapping called the Hopf fibration, which wraps the 3-sphere S3 around the usual sphere S2 in a non-trivial...

curvature, Ricci flat Ricci decomposition Schouten tensor Weyl curvature Ricci flow Einstein manifold Holonomy Gauss–Bonnet theorem Hopf–Rinow theorem Cartan–Hadamard...

strain, cubane is kinetically stable, due to a lack of readily available decomposition paths. Angle strain would make an octahedron highly unstable due to...

2013, studied the decomposition of regular 4-polytopes into honeycombs of tori tiling the Clifford torus which correspond to Hopf fibrations. Banchoff...

study of their complements, and in turn into 3-manifold theory. The JSJ decomposition and Thurston's hyperbolization theorem reduces the study of knots in...

center. Levi decomposition Hazewinkel, Michiel; Gubareni, Nadiya; Kirichenko, V. V. (2010), Algebras, Rings and Modules: Lie Algebras and Hopf Algebras,...