Massimo Furi | Università degli Studi di Firenze (University of Florence) (original) (raw)

Uploads

Papers by Massimo Furi

Research paper thumbnail of A Lefschetz type theorem for the minimal displacement of points under maps defined on a class of ANR’s

Research paper thumbnail of On the minimal displacement under acyclic-valued maps defined on a class of ANR’s

Research paper thumbnail of Successioni di trasformazioni in uno spazio metrico e punti fissi (Successive transformations in a metric space and fixed points)

Research paper thumbnail of Some characteristic properties of real Hilbert spaces

Revue Roumaine des Mathematiques Pures et Appliquees

Research paper thumbnail of Periodic solutions for the equation x ¨+f(x)x ˙ 2 +g(x)=0

Research paper thumbnail of On a property of the unit sphere in a linear normed space

Research paper thumbnail of Handbook of topological fixed point theory

Research paper thumbnail of Stably-solvable operators in Banach spaces

Research paper thumbnail of A fixed point theorem in complete metric space

Research paper thumbnail of On α-Lipschitz retractions of the unit closed ball onto its boundary

Research paper thumbnail of Fixed points for densifying mappings

Research paper thumbnail of On the minimal displacement of points under α-Lipschitz maps in normed spaces

Research paper thumbnail of About the solvability of ordinary differential equations with asymptotic boundary conditions

Research paper thumbnail of Components of positive solutions for non-linear equations with several parameters

Research paper thumbnail of About asymptotic problems for ordinary differential equations

Bollettino della Unione Matematica Italiana B

Research paper thumbnail of A simple notion of orientability for Fredholm maps of index zero between Banach manifolds and degree theory

Annales des Sciences Mathematiques du Quebec

Dans cette note on donne une définition du degré topologique pour une classe d'applications (nomm... more Dans cette note on donne une définition du degré topologique pour une classe d'applications (nommées orientables) de Fredholm d'indice zéro entre des variétés de Banach réelles.

Research paper thumbnail of On the concept of orientability for Fredholm maps between real Banach manifolds

Topological methods in nonlinear analysis

In [1] we introduced a concept of orientation and topological degree for nonlinear Fredholm maps ... more In [1] we introduced a concept of orientation and topological degree for nonlinear Fredholm maps between real Banach manifolds. In this paper we study properties of this notion of orientation and we compare it with related results due to Elworthy-Tromba and Fitzpatrick-Pejsachowicz-Rabier.

Research paper thumbnail of The invariance of domain for C 1 Fredholm maps of index zero

Dedicated to Alfonso Vignoli on the occasion of his 60th anniversary Summary: We give a version o... more Dedicated to Alfonso Vignoli on the occasion of his 60th anniversary Summary: We give a version of the classical Invariance of Domain Theorem for nonlinear Fredholm maps of index zero between Banach spaces (and Banach manifolds). The proof is based on a finite dimensional reduction technique combined with a mod 2 degree argument for continuous maps between (finite dimensional) differentiable manifolds.

Research paper thumbnail of BIFURCATION RESULTS FOR FAMILIES OF FREDHOLM MAPS OF INDEX ZERO BETWEEN BANACH SPACES

Research paper thumbnail of Chaotic orbits of a pendulum with variable length

Electronic Journal of Differential Equations

The main purpose of this investigation is to show that a pendulum, whose pivot oscillates vertica... more The main purpose of this investigation is to show that a pendulum, whose pivot oscillates vertically in a periodic fashion, has uncountably many chaotic orbits. The attribute chaotic is given according to the criterion we now describe. First, we associate to any orbit a finite or infinite sequence as follows. We write 1 or −1 every time the pendulum crosses the position of unstable equilibrium with positive (counterclockwise) or negative (clockwise) velocity, respectively. We write 0 whenever we find a pair of consecutive zero's of the velocity separated only by a crossing of the stable equilibrium, and with the understanding that different pairs cannot share a common time of zero velocity. Finally, the symbol ω, that is used only as the ending symbol of a finite sequence, indicates that the orbit tends asymptotically to the position of unstable equilibrium. Every infinite sequence of the three symbols {1, −1, 0} represents a real number of the interval [0, 1] written in base 3 when −1 is replaced with 2. An orbit is considered chaotic whenever the associated sequence of the three symbols {1, 2, 0} is an irrational number of [0, 1]. Our main goal is to show that there are uncountably many orbits of this type.

Research paper thumbnail of A Lefschetz type theorem for the minimal displacement of points under maps defined on a class of ANR’s

Research paper thumbnail of On the minimal displacement under acyclic-valued maps defined on a class of ANR’s

Research paper thumbnail of Successioni di trasformazioni in uno spazio metrico e punti fissi (Successive transformations in a metric space and fixed points)

Research paper thumbnail of Some characteristic properties of real Hilbert spaces

Revue Roumaine des Mathematiques Pures et Appliquees

Research paper thumbnail of Periodic solutions for the equation x ¨+f(x)x ˙ 2 +g(x)=0

Research paper thumbnail of On a property of the unit sphere in a linear normed space

Research paper thumbnail of Handbook of topological fixed point theory

Research paper thumbnail of Stably-solvable operators in Banach spaces

Research paper thumbnail of A fixed point theorem in complete metric space

Research paper thumbnail of On α-Lipschitz retractions of the unit closed ball onto its boundary

Research paper thumbnail of Fixed points for densifying mappings

Research paper thumbnail of On the minimal displacement of points under α-Lipschitz maps in normed spaces

Research paper thumbnail of About the solvability of ordinary differential equations with asymptotic boundary conditions

Research paper thumbnail of Components of positive solutions for non-linear equations with several parameters

Research paper thumbnail of About asymptotic problems for ordinary differential equations

Bollettino della Unione Matematica Italiana B

Research paper thumbnail of A simple notion of orientability for Fredholm maps of index zero between Banach manifolds and degree theory

Annales des Sciences Mathematiques du Quebec

Dans cette note on donne une définition du degré topologique pour une classe d'applications (nomm... more Dans cette note on donne une définition du degré topologique pour une classe d'applications (nommées orientables) de Fredholm d'indice zéro entre des variétés de Banach réelles.

Research paper thumbnail of On the concept of orientability for Fredholm maps between real Banach manifolds

Topological methods in nonlinear analysis

In [1] we introduced a concept of orientation and topological degree for nonlinear Fredholm maps ... more In [1] we introduced a concept of orientation and topological degree for nonlinear Fredholm maps between real Banach manifolds. In this paper we study properties of this notion of orientation and we compare it with related results due to Elworthy-Tromba and Fitzpatrick-Pejsachowicz-Rabier.

Research paper thumbnail of The invariance of domain for C 1 Fredholm maps of index zero

Dedicated to Alfonso Vignoli on the occasion of his 60th anniversary Summary: We give a version o... more Dedicated to Alfonso Vignoli on the occasion of his 60th anniversary Summary: We give a version of the classical Invariance of Domain Theorem for nonlinear Fredholm maps of index zero between Banach spaces (and Banach manifolds). The proof is based on a finite dimensional reduction technique combined with a mod 2 degree argument for continuous maps between (finite dimensional) differentiable manifolds.

Research paper thumbnail of BIFURCATION RESULTS FOR FAMILIES OF FREDHOLM MAPS OF INDEX ZERO BETWEEN BANACH SPACES

Research paper thumbnail of Chaotic orbits of a pendulum with variable length

Electronic Journal of Differential Equations

The main purpose of this investigation is to show that a pendulum, whose pivot oscillates vertica... more The main purpose of this investigation is to show that a pendulum, whose pivot oscillates vertically in a periodic fashion, has uncountably many chaotic orbits. The attribute chaotic is given according to the criterion we now describe. First, we associate to any orbit a finite or infinite sequence as follows. We write 1 or −1 every time the pendulum crosses the position of unstable equilibrium with positive (counterclockwise) or negative (clockwise) velocity, respectively. We write 0 whenever we find a pair of consecutive zero's of the velocity separated only by a crossing of the stable equilibrium, and with the understanding that different pairs cannot share a common time of zero velocity. Finally, the symbol ω, that is used only as the ending symbol of a finite sequence, indicates that the orbit tends asymptotically to the position of unstable equilibrium. Every infinite sequence of the three symbols {1, −1, 0} represents a real number of the interval [0, 1] written in base 3 when −1 is replaced with 2. An orbit is considered chaotic whenever the associated sequence of the three symbols {1, 2, 0} is an irrational number of [0, 1]. Our main goal is to show that there are uncountably many orbits of this type.

Log In