Search results for "Saddle"
showing 10 items of 74 documents
Angular spectrum of diffracted wave fields with apochromatic correction.
2008
We report on compensation of diffraction-induced angular dispersion of ultrashort pulses up to a second order. A strategy for chromatic correction profits from high dispersion of kinoform-type zone plates. Ultraflat dispersion curves rely on a saddle point that may be tuned at a prescribed wavelength. Validity of our approach may reach the few-cycles regime.
Plane foliations with a saddle singularity
2012
Abstract We study the set of planar vector fields with a unique singularity of hyperbolic saddle type. We found conditions to assure that a such vector field is topologically equivalent to a linear saddle. Furthermore, we describe the plane foliations associated to these vector fields. Such a foliation can be split in two subfoliations. One without restriction and another one that is topologically characterized by means of trees.
Blenders near polynomial product maps of $\mathbb C^2$
2021
In this paper we show that if $p$ is a polynomial which bifurcates then the product map $(z,w)\mapsto(p(z),q(w))$ can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets can be chosen to be of two types : repelling or saddle. As a consequence, such product map belongs to the closure of the interior of two different sets : the bifurcation locus of $H_d(\mathbb P^2)$ and the set of endomorphisms having an attracting set of non-empty interior. In an independent part, we use perturbations of H\'enon maps to obtain examples of attracting sets with repelling points and also of quasi-attractors which are not attracting sets.
Performance of a historical cantilever reinforced concrete bridge with half-joint degradation
2022
The lack of maintenance of roadway concrete bridges built from the Second World War until the 70 s of the 20th century has led in recent years to an ever-increasing request for safety assessments. When bridge performance in terms of Serviceability Limit State (SLS) and Ultimate Limit State (ULS) has to be evaluated, in-situ visual inspections and load tests for safety and maintenance assessment have to be coupled with structural analysis. In order to identify a sound bridge structural model and to assess the actual conservation state, more refined models than those usually considered for section and reinforcement design should be used to reproduce the results of load tests and perform globa…
Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems
2015
In this paper we introduce new methods to prove the finite cyclicity of some graphics through a triple nilpotent point of saddle or elliptic type surrounding a center. After applying a blow-up of the family, yielding a singular 3-dimensional foliation, this amounts to proving the finite cyclicity of a family of limit periodic sets of the foliation. The boundary limit periodic sets of these families were the most challenging, but the new methods are quite general for treating such graphics. We apply these techniques to prove the finite cyclicity of the graphic $(I_{14}^1)$, which is part of the program started in 1994 by Dumortier, Roussarie and Rousseau (and called DRR program) to show that…
A C1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources
2003
We show that, for every compact n-dimensional manifold, n > 1, there is a residual subset of Diff (M) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies one of the following two possibilities: Either it is contained in the closure of an infinite set of sinks or sources (Newhouse phenomenon), or it presents some weak form of hyperbolicity called dominated splitting (this is a generalization of a bidimensional result of Mafine [Ma3]). In particular, we show that any Cl-robustly transitive diffeomorphism admits a dominated splitting.
Landesman-Lazer type (p, q)-equations with Neumann condition
2020
We consider a Neumann problem driven by the (p, q)-Laplacian under the Landesman-Lazer type condition. Using the classical saddle point theorem and other classical results of the calculus of variations, we show that the problem has at least one nontrivial weak solution.
Singular levels and topological invariants of Morse Bott integrable systems on surfaces
2016
Abstract We classify up to homeomorphisms closed curves and eights of saddle points on orientable closed surfaces. This classification is applied to Morse Bott foliations and Morse Bott integrable systems allowing us to define a complete invariant. We state also a realization Theorem based in two transformations and one generator (the foliation of the sphere with two centers).
Transition structures for hydride transfer reactions in vacuo and their role in enzyme catalysis
1996
A general discussion as to the role of in vacuo transition structure in enzyme catalysis is presented. Quantum mechanical aspects are emphasized. The transition structures defined as saddle points ...
Applicazione delle Linee guida italiane alle valutazioni di sicurezza strutturale del ponte Corleone sulla tangenziale di Palermo
2022
The "nominal life" of a large part of existing reinforced and prestressed concrete bridges, in Italy, is expiring, often in the absence of ordinary or extraordinary maintenance. Consequently, the Italian infrastructural network is in a critical phase, followed by the alarmed awareness of the public opinion, especially after the collapse of the Polcevera viaduct. Specific guidelines on risk classifi-cation, management, safety assessment, monitoring of existing bridges have been issued by the Superior Council of Public Works in 2020, to address the emergency. Between ‘50s and ‘70s of the last century, important examples of reinforced and prestressed concrete bridges were built in Italy by the…