The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Vincent Guedj - One of the best experts on this subject based on the ideXlab platform.
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dynamics of meromorphic mappings with small Topological Degree ii energy and invariant measure
Commentarii Mathematici Helvetici, 2011Co-Authors: Jeffrey Diller, Romain Dujardin, Vincent GuedjAbstract:We continue our study of the dynamics of meromorphic mappings with small Topological Degree ?2(f)polynomial endomorphism of C2. They are new even in the birational case (?2(f)=1). We also exhibit families of mappings where our assumptions are generically satisfied and show that if counterexamples exist, the corresponding measure must give mass to a pluripolar set.
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ergodic properties of rational mappings with large Topological Degree
Annals of Mathematics, 2005Co-Authors: Vincent GuedjAbstract:Let X be a projective manifold and f : X ?? X a rational mapping with large Topological Degree, dt > ?Ek.1(f) := the (k . 1)th dynamical Degree of f. We give an elementary construction of a probability measure ?Ef such that d.n t (fn).?? ?? ?Ef for every smooth probability measure ?? on X. We show that every quasiplurisubharmonic function is ?Ef -integrable. In particular ?Ef does not charge either points of indeterminacy or pluripolar sets, hence ?Ef is f-invariant with constant jacobian f.?Ef = dt?Ef . We then establish the main ergodic properties of ?Ef : it is mixing with positive Lyapunov exponents, preimages of ?hmost?h points as well as repelling periodic points are equidistributed with respect to ?Ef . Moreover, when dimC X . 3 or when X is complex homogeneous, ?Ef is the unique measure of maximal entropy.
Jian-zhong Xiao - One of the best experts on this subject based on the ideXlab platform.
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Condensing operators and Topological Degree theory in standard fuzzy normed spaces
Fuzzy Sets and Systems, 2010Co-Authors: Jian-zhong Xiao, Ying LuAbstract:In this paper level-cut measures of noncompactness are introduced in standard fuzzy normed spaces and condensing operators are studied. Using the extensions of nonlinear compact operators, Topological Degree theory with respect to condensing operators is given in standard fuzzy normed spaces. As an application of Degree theory, a fixed point theorem for condensing operators is presented.
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Topological Degree theory and fixed point theorems in fuzzy normed space
Fuzzy Sets and Systems, 2004Co-Authors: Jian-zhong XiaoAbstract:Abstract In this paper, the Leray–Schauder Topological Degree theory is developed in a fuzzy normed space. Since the linear topology on this fuzzy normed space is not necessarily locally convex, and since each Menger probabilistic normed space can be considered as a special fuzzy normed space, the Degree theory in this paper is different from the Degree theory in locally convex linear Topological space presented by Nagumo (Amer. J. Math. 73 (1951) 497–511), and it also is an extension of the Degree theory in Menger probabilistic normed space studied by Zhang and Chen (Appl. Math. Mech. 10(6) (1989) 477–486). Applying this Degree theory, some fixed point theorems for operators are given in fuzzy normed spaces, and some former corresponding results are extended and improved.
M N Vrahatis - One of the best experts on this subject based on the ideXlab platform.
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Topological Degree theory and local analysis of area preserving maps
Chaos, 2003Co-Authors: C. Polymilis, G. Servizi, Ch. Skokos, Giorgio Turchetti, M N VrahatisAbstract:We consider methods based on the Topological Degree theory to compute periodic orbits of area preserving maps. Numerical approximations to the Kronecker integral give the number of fixed points of the map provided that the integration step is “small enough.” Since in any neighborhood of a fixed point the map gets four different combinations of its algebraic signs we use points on a lattice to detect the candidate fixed points by selecting boxes whose corners show all combinations of signs. This method and the Kronecker integral can be applied to bounded continuous maps such as the beam–beam map. On the other hand, they cannot be applied to maps defined on the torus, such as the standard map which has discontinuity curves propagating by iteration. Although the use of the characteristic bisection method is, in some cases, unable to detect all fixed points up to a given order, their distribution gives us a clear picture of the dynamics of the map.
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on the complexity of isolating real roots and computing with certainty the Topological Degree
Journal of Complexity, 2002Co-Authors: Bernard Mourrain, M N Vrahatis, Jean-claude YakoubsohnAbstract:In this contribution the isolation of real roots and the computation of the Topological Degree in two dimensions are considered and their complexity is analyzed. In particular, we apply Stenger's Degree computational method by splitting properly the boundary of the given region to obtain a sequence of subintervals along the boundary that forms a sufficient refinement. To this end, we properly approximate the function using univariate polynomials. Then we isolate each one of the zeros of these polynomials on the boundary of the given region in various subintervals so that these subintervals form a sufficiently refined boundary.
Mohammad Reza Salehi - One of the best experts on this subject based on the ideXlab platform.
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fuzzy compact operators and Topological Degree theory
Fuzzy Sets and Systems, 2009Co-Authors: Ildar Sadeqi, Mohammad Reza SalehiAbstract:In this paper we first prove that the definition of fuzzy norm continuity and fuzzy boundedness of linear operators are equivalent. We show that the continuity assumption in the definition of compact linear operator is not necessary. We also point out that there is a gap in the proof of a theorem of Xiao and Zhu and we give a corrected version of the theorem such that all results based on the revised theorem remain true. Furthermore, we define a fuzzy product norm on the Cartesian product of two fuzzy normed spaces and prove a multiplicative property for the Leray-Schauder Topological Degree.
Jean-claude Yakoubsohn - One of the best experts on this subject based on the ideXlab platform.
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Isolation of Real Roots and Computation of the Topological Degree
2020Co-Authors: Bernard Mourrain, Michael N. Vrahatis, Jean-claude YakoubsohnAbstract:In this work, the isolation of real rootsbased on Bernstein polynomials, and the computation of the Topological Degree in two dimensions are considered and their complexity is analyzed. In particular, we apply Stenger's Degree computational method by splitting properly the boundary of the given region to obtain a sequence of subintervals along the boundary that forms a sufficien- t refinement. To this end, we properly approximate the function using univariate polynomials. Then we isolate each one of the zeros of these polynomials on the boundary of the given region in various subintervals so that these subintervals form a sufficiently refined boundary.
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on the complexity of isolating real roots and computing with certainty the Topological Degree
Journal of Complexity, 2002Co-Authors: Bernard Mourrain, M N Vrahatis, Jean-claude YakoubsohnAbstract:In this contribution the isolation of real roots and the computation of the Topological Degree in two dimensions are considered and their complexity is analyzed. In particular, we apply Stenger's Degree computational method by splitting properly the boundary of the given region to obtain a sequence of subintervals along the boundary that forms a sufficient refinement. To this end, we properly approximate the function using univariate polynomials. Then we isolate each one of the zeros of these polynomials on the boundary of the given region in various subintervals so that these subintervals form a sufficiently refined boundary.
