### Some remarks on degree theory for ${\text{\rm SO}(2)}$-equivariant transversal maps

#### Abstract

The aim of this article is to introduce a new class $\text{\rm SO}(2)$-equivariant

transversal maps $\text{\rm cl}(\Omega),\partial \Omega)$ and to define

degree theory for such maps. We define degree for $\text{\rm SO}(2)$-equivariant transversal maps and prove some properties

of this invariant. Moreover, we characterize $\text{\rm SO}(2)$-equivariant transversal isomorphisms and derive formula

for degree of such isomorphisms.

transversal maps $\text{\rm cl}(\Omega),\partial \Omega)$ and to define

degree theory for such maps. We define degree for $\text{\rm SO}(2)$-equivariant transversal maps and prove some properties

of this invariant. Moreover, we characterize $\text{\rm SO}(2)$-equivariant transversal isomorphisms and derive formula

for degree of such isomorphisms.

#### Keywords

Equivariant degree theory; equivariant bifurcation theory

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