We associate to a parametrized family $f$ of nonlinear Fredholm maps possessing a trivial branch of zeroes an {\it index of bifurcation} $\beta(f)$ which provides an algebraic measure for the number of bifurcation points from the trivial branch. The index $\beta(f)$ is derived from the index bundle of the linearization of the family along the trivial branch by means of the generalized $J$-homomorphism. Using the Agranovich reduction and a cohomological form of the Atiyah-Singer family index theorem, due to Fedosov, we compute the bifurcation index of a multiparameter family of nonlinear elliptic boundary value problems from the principal symbol of the linearization along the trivial branch. In this way we obtain criteria for ...
Abstract: Bifurcations in the families of local Fredholm analytic operators are considered...
AbstractA sufficient condition for bifurcation of real solutions of G(λ, u) = 0 (where G: R × D → E,...
The author considers an orientable, compact, connected, n-dimensional manifold X and a family of fun...
I will shortly discuss an approach to bifurcation theory based on elliptic topology. The main go...
AbstractWe obtain some new bifurcation criteria for solutions of general boundary value problems for...
We obtain some new criteria for bifurcation of solutions of general boundary value problems ...
Abstract. We present three criteria for bifurcation from infinity of solutions of general boundary ...
We show that a family $F_p;\ p\in P$ of nonlinear elliptic boundary value problems of index $0$ par...
Abstract. We show that a family Fp; p ∈ P of nonlinear elliptic boundary value problems of index 0 p...
We obtain an estimate for the covering dimension of the set of bifurcation points for solutions of ...
We modify an argument for multiparameter bifurcation of Fredholm maps by Fitzpatrick and Pejsachowic...
We develop a K-theoretic approach to multiparameter bifurcation theory of homoclinic solutions of di...
We modify an argument for multiparameter bifurcation of Fredholm maps by Fitzpatrick and Pejsachowic...
We compute the parity of a path of Fredholm operators in terms of its index bundle. The result is ap...
AbstractIn this paper we give a result in multiparameter local bifurcation theory. This result is a ...
Abstract: Bifurcations in the families of local Fredholm analytic operators are considered...
AbstractA sufficient condition for bifurcation of real solutions of G(λ, u) = 0 (where G: R × D → E,...
The author considers an orientable, compact, connected, n-dimensional manifold X and a family of fun...
I will shortly discuss an approach to bifurcation theory based on elliptic topology. The main go...
AbstractWe obtain some new bifurcation criteria for solutions of general boundary value problems for...
We obtain some new criteria for bifurcation of solutions of general boundary value problems ...
Abstract. We present three criteria for bifurcation from infinity of solutions of general boundary ...
We show that a family $F_p;\ p\in P$ of nonlinear elliptic boundary value problems of index $0$ par...
Abstract. We show that a family Fp; p ∈ P of nonlinear elliptic boundary value problems of index 0 p...
We obtain an estimate for the covering dimension of the set of bifurcation points for solutions of ...
We modify an argument for multiparameter bifurcation of Fredholm maps by Fitzpatrick and Pejsachowic...
We develop a K-theoretic approach to multiparameter bifurcation theory of homoclinic solutions of di...
We modify an argument for multiparameter bifurcation of Fredholm maps by Fitzpatrick and Pejsachowic...
We compute the parity of a path of Fredholm operators in terms of its index bundle. The result is ap...
AbstractIn this paper we give a result in multiparameter local bifurcation theory. This result is a ...
Abstract: Bifurcations in the families of local Fredholm analytic operators are considered...
AbstractA sufficient condition for bifurcation of real solutions of G(λ, u) = 0 (where G: R × D → E,...
The author considers an orientable, compact, connected, n-dimensional manifold X and a family of fun...