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Papers by josé manuel Salazar

Journal of Fixed Point Theory and Applications

Transactions of the American Mathematical Society

Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. ... more Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. In this paper we study the fixed point index of the map that f induces in the n-symmetric product of X, F n (X). This index can detect the existence of periodic orbits of period ≤ n of f , and it can be used to obtain the Euler characteristic of the n-symmetric product of a manifold X, χ(F n (X)). We compute χ(F n (X)) for all orientable compact surfaces without boundary.

Topology and its Applications, 2004

Let U⊂R2 be an open subset and let f:U→f(U)⊂R2 be a homeomorphism. Let M=M1∪⋯∪Mr⊂U be a disjoint ... more Let U⊂R2 be an open subset and let f:U→f(U)⊂R2 be a homeomorphism. Let M=M1∪⋯∪Mr⊂U be a disjoint union of discs that isolates the invariant compactum K. The aim of this paper is to study the dynamics of f in K and to use the fixed point index to detect, in a simple and geometric way, the existence of periodic orbits

Journal of Differential Equations, 2008

Given any positive sequence {c n } n∈N , we construct orientation preserving homeomorphisms f : R... more Given any positive sequence {c n } n∈N , we construct orientation preserving homeomorphisms f : R 3 → R 3 such that F ix(f) = P er(f) = {0}, 0 is Lyapunov stable and lim sup |i(f m ,0)| cm = ∞. We will use our results to discuss and to point out some strong dierences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.

Fixed Point Theory and Applications, 2010

Let U ⊂ R 2 be an open subset and f : U → R 2 be an arbitrary local homeomorphism with Fix f {p}.... more Let U ⊂ R 2 be an open subset and f : U → R 2 be an arbitrary local homeomorphism with Fix f {p}. We compute the fixed point indices of the iterates of f at p, i R 2 f k , p , and we identify these indices in dynamical terms. Therefore, we obtain a sort of Poincaré index formula without differentiability assumptions. Our techniques apply equally to both orientation preserving and orientation reversing homeomorphisms. We present some new results, especially in the orientation reversing case.

Ergodic Theory and Dynamical Systems, 2006

ABSTRACT

Ergodic Theory and Dynamical Systems, 2005

We use a notion (introduced in Topology 41 (2002), 1119-1212), which is stronger than the concept... more We use a notion (introduced in Topology 41 (2002), 1119-1212), which is stronger than the concept of filtration pair, to prove a stable/unstable manifold general theorem for local homeomorphisms of the plane in a neighborhood of an isolated fixed point.

Topology and Its Applications, 2004

Let U⊂R2 be an open subset and let f:U→f(U)⊂R2 be a homeomorphism. Let M=M1∪⋯∪Mr⊂U be a disjoint ... more Let U⊂R2 be an open subset and let f:U→f(U)⊂R2 be a homeomorphism. Let M=M1∪⋯∪Mr⊂U be a disjoint union of discs that isolates the invariant compactum K. The aim of this paper is to study the dynamics of f in K and to use the fixed point index to detect, in a simple and geometric way, the existence of periodic orbits

Ergodic Theory and Dynamical Systems, 2005

We use a notion (introduced in Topology 41 (2002), 1119-1212), which is stronger than the concept... more We use a notion (introduced in Topology 41 (2002), 1119-1212), which is stronger than the concept of filtration pair, to prove a stable/unstable manifold general theorem for local homeomorphisms of the plane in a neighborhood of an isolated fixed point.

Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we construct orientation preserving homeo... more Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we construct orientation preserving homeomorphisms (f:{\Bbb R}^3 \to {\Bbb R}^3) such that (Fix(f)=Per(f)=\{0\}), (0) is Lyapunov stable and (\limsup \frac{|i(f^m, 0)|}{c_m}= \infty). We will use our results to discuss and to point out some strong differences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.

Dedicated to professor José M. Montesinos in the occasion of his 65th birthday and to the memory ... more Dedicated to professor José M. Montesinos in the occasion of his 65th birthday and to the memory of professor Julián Martínez.

Journal of Fixed Point Theory and Applications

Transactions of the American Mathematical Society

Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. ... more Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. In this paper we study the fixed point index of the map that f induces in the n-symmetric product of X, F n (X). This index can detect the existence of periodic orbits of period ≤ n of f , and it can be used to obtain the Euler characteristic of the n-symmetric product of a manifold X, χ(F n (X)). We compute χ(F n (X)) for all orientable compact surfaces without boundary.

Topology and its Applications, 2004

Let U⊂R2 be an open subset and let f:U→f(U)⊂R2 be a homeomorphism. Let M=M1∪⋯∪Mr⊂U be a disjoint ... more Let U⊂R2 be an open subset and let f:U→f(U)⊂R2 be a homeomorphism. Let M=M1∪⋯∪Mr⊂U be a disjoint union of discs that isolates the invariant compactum K. The aim of this paper is to study the dynamics of f in K and to use the fixed point index to detect, in a simple and geometric way, the existence of periodic orbits

Journal of Differential Equations, 2008

Given any positive sequence {c n } n∈N , we construct orientation preserving homeomorphisms f : R... more Given any positive sequence {c n } n∈N , we construct orientation preserving homeomorphisms f : R 3 → R 3 such that F ix(f) = P er(f) = {0}, 0 is Lyapunov stable and lim sup |i(f m ,0)| cm = ∞. We will use our results to discuss and to point out some strong dierences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.

Fixed Point Theory and Applications, 2010

Let U ⊂ R 2 be an open subset and f : U → R 2 be an arbitrary local homeomorphism with Fix f {p}.... more Let U ⊂ R 2 be an open subset and f : U → R 2 be an arbitrary local homeomorphism with Fix f {p}. We compute the fixed point indices of the iterates of f at p, i R 2 f k , p , and we identify these indices in dynamical terms. Therefore, we obtain a sort of Poincaré index formula without differentiability assumptions. Our techniques apply equally to both orientation preserving and orientation reversing homeomorphisms. We present some new results, especially in the orientation reversing case.

Ergodic Theory and Dynamical Systems, 2006

ABSTRACT

Ergodic Theory and Dynamical Systems, 2005

We use a notion (introduced in Topology 41 (2002), 1119-1212), which is stronger than the concept... more We use a notion (introduced in Topology 41 (2002), 1119-1212), which is stronger than the concept of filtration pair, to prove a stable/unstable manifold general theorem for local homeomorphisms of the plane in a neighborhood of an isolated fixed point.

Topology and Its Applications, 2004

Let U⊂R2 be an open subset and let f:U→f(U)⊂R2 be a homeomorphism. Let M=M1∪⋯∪Mr⊂U be a disjoint ... more Let U⊂R2 be an open subset and let f:U→f(U)⊂R2 be a homeomorphism. Let M=M1∪⋯∪Mr⊂U be a disjoint union of discs that isolates the invariant compactum K. The aim of this paper is to study the dynamics of f in K and to use the fixed point index to detect, in a simple and geometric way, the existence of periodic orbits

Ergodic Theory and Dynamical Systems, 2005

We use a notion (introduced in Topology 41 (2002), 1119-1212), which is stronger than the concept... more We use a notion (introduced in Topology 41 (2002), 1119-1212), which is stronger than the concept of filtration pair, to prove a stable/unstable manifold general theorem for local homeomorphisms of the plane in a neighborhood of an isolated fixed point.

Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we construct orientation preserving homeo... more Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we construct orientation preserving homeomorphisms (f:{\Bbb R}^3 \to {\Bbb R}^3) such that (Fix(f)=Per(f)=\{0\}), (0) is Lyapunov stable and (\limsup \frac{|i(f^m, 0)|}{c_m}= \infty). We will use our results to discuss and to point out some strong differences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.

Dedicated to professor José M. Montesinos in the occasion of his 65th birthday and to the memory ... more Dedicated to professor José M. Montesinos in the occasion of his 65th birthday and to the memory of professor Julián Martínez.