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We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers,…
We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions…
Given an increasing odd homeomorphism $\sigma$ : R $\rightarrow$ R, the two bijective maps h $\sigma$ , v $\sigma$ : R 2 $\rightarrow$ R 2 dened by h $\sigma$ (x, y) = (x + $\sigma$ --1 (y), y) and v $\sigma$ (x, y) = (x, $\sigma$(x) + y).…
Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…
The statistics of a passive scalar randomly emitted from a point source is investigated analytically. Our attention has been focused on the two-point equal-time scalar correlation function. The latter is indeed easily related to the…
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
A non-autonomous version of the standard map with a periodic variation of the parameter is introduced and studied. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
An analytico-geometric reflection principle is established by means of normal deformations of analytic discs.
We study Yamabe metrics, and the moduli space of Yamabe metrics, on an arbitrary closed 3-manifold M. The main focus is on the boundary behavior of the moduli space, i.e. the behavior of degenerating sequences of unit volume Yamabe metrics…
It is well known that for analytic cost functions, gradient flow trajectories have finite length and converge to a single critical point. The gradient conjecture of R. Thom states that, again for analytic cost functions, whenever the…
This paper is devoted to the investigation of inverse problems related to stationary drift-diffusion equations modeling semiconductor devices. In this context we analyze several identification problems corresponding to different types of…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…
In this paper, we study a connection between disintegration of measures and geometric properties of probability spaces. We prove a disintegration theorem, addressing disintegration from the perspective of an optimal transport problem. We…
We study polynomial planar systems with singularity of focus type without characteristic directions. Simple and natural transformation of weak focus has been used to obtain such degenerate focus. We compute the box dimension of a spiral…
We consider the parameterization ${\mathbf{f}}=(f_0,f_1,f_2)$ of a plane rational curve $C$ of degree $n$, and we want to study the singularities of $C$ via such parameterization. We do this by using the projection from the rational normal…
We study the singularity of Quillen metrics for one-parameter degenerations of compact Kaehler manifolds.
Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become…