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A Bound for the Fixed-Point Index of an Area-Preserving Map with Applications to Mechanics.

Inventiones mathematicae

A counterexample to the smoothness of the solution to an equation arising in fluid mechanics

Commentationes Mathematicae Universitatis Carolinae

We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the back to coordinates map'' may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for...

A degree for a class of acyclic-valued vector fields in Banach spaces

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

A degree theory for almost continuous functions

Fundamenta Mathematicae

A fixed point index for bimaps

Fundamenta Mathematicae

A Fixed Point Index Theory for Symmetric Product Mappings.

Manuscripta mathematica

A Lefschetz-type coincidence theorem

Fundamenta Mathematicae

A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: ${I}_{fg}={\lambda }_{fg}$, that is, the coincidence index is equal to the Lefschetz number. It follows that if ${\lambda }_{fg}\ne 0$ then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like” (acyclic)...

A note on symmetric maps for spheres.

Mathematica Scandinavica

A Poincaré formula for the fixed point indices of the iterates of arbitrary planar homeomorphisms.

Fixed Point Theory and Applications [electronic only]

A Rapid Generalized Method of Bisection for Solving Systems of Non-linear Equations.

Numerische Mathematik

A simple proof of the degree formula for (Z/p)-equivariant maps.

Mathematische Zeitschrift

A Simplification of Stenger's Topological Degree Formula.

Numerische Mathematik

Addendum to: A Bound for the Fixed-Point Index of an Area-Preserving Map with Applications to Mechanics.

Inventiones mathematicae

An algebraic method for calculating the topological degree

Banach Center Publications

An Efficient Degree-Computation Method for a Generalized Method of Bisection.

Numerische Mathematik

Bourgin–Yang-type theorem for $a$-compact perturbations of closed operators. I: The case of index theories with dimension property.

Abstract and Applied Analysis

Brouwer degree, equivariant maps and tensor powers.

Abstract and Applied Analysis

Coincidence index for fiber-preserving maps an approach to stable cohomotopy.

Manuscripta mathematica

Computer calculation of the degree of maps into the Poincaré homology sphere.

Experimental Mathematics

Computing the Topological Degree of a Mapping in Rn .

Numerische Mathematik

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