1 citations · 1 across the 7 of their papers we have counts for
7 papers
Homology groups of filtrations
Peter Saveliev
Such modern applications of topology as data analysis and digital image analysis have to deal with noise and other uncertainty. In this environment, topological spaces often appear…
Applications of Lefschetz numbers in control theory
Peter Saveliev
We develop some applications of techniques of the Lefschetz coincidence theory in control theory. The topics are existence of equilibria and their robustness, controllability and i…
Higher order Nielsen numbers
Peter Saveliev
Suppose X,Y are manifolds, f,g:X->Y are maps. The well-known Coincidence Problem studies the coincidence set C={x:f(x)=g(x)}. The number m=dimX-dimY is called the codimension of th…
Removing coincidences of maps between manifolds of different dimensions
Peter Saveliev
We consider sufficient conditions of local removability of coincidences of maps f,g:N->M, where M,N are manifolds with dimensions dimN>dimM. The coincidence index is the only obstr…
Lomonosov's Invariant Subspace Theorem for Multivalued Linear Operators
Peter Saveliev
The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator…
Lefschetz Coincidence Theory for Maps Between Spaces of Different Dimensions
Peter Saveliev
For a given pair of maps f,g:X->M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism L:H(X)->H(M) of degree (-n). We…