Related papers: How roundoff errors help to compute the rotation s…
This paper is concerned with the robust tracking control of linear uncertain systems, whose unknown system parameters and disturbances are bounded within ellipsoidal sets. We propose an adaptive robust control that can actively learn the…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
In this paper, we propose a novel approach for computing robust backward reachable sets from noisy data for unknown constrained linear systems subject to bounded disturbances. In particular, we develop an algorithm for obtaining zonotopic…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…
We study the dynamics of iteration function systems generated by a pair of circle diffeomorphisms close to rotations in the $C^{1+\mathrm{bv}}$-topology. We characterize the obstruction to minimality and describe the limit set. In…
In this paper we generalize the discrete r-homotopy to the discrete (s, r)-homotopy. Then by this notion, we introduce the discrete motion planning for robots which can move discreetly. Moreover, in this case the number of motion planning,…
Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical…
This article consists in applications of [arXiv:2511.14232] in the case of homemomorphisms of higher genus surfaces whose homological rotation set is big enough -- a class of dynamics that is open. We first prove a structure theorem for the…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…
This work is concerned with optimal control problems where the objective functional consists of a tracking-type functional and an additional "multibang" regularization functional that promotes optimal control taking values from a given…
In this paper we investigate fixed-point numbers and entropies of endomorphisms on abelian varieties. It was shown quite recently that the number of fixed-points of an iterated endomorphism on a simple complex torus is either periodic or…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
The authors show that the round-off error can break the consistency which is the premise of using the difference equation to replace the original differential equations. We therefore proposed a theoretical approach to investigate this…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
We prove that a homeomorphism of the torus homotopic to the identity whose rotation set is reduced to a single totally irrational vector is chain-recurrent. In fact, we show that pseudo-orbits can be chosen with a small number of jumps, in…
We provide a complete characterization of periodic point free homeomorphisms of the $2$-torus admitting irrational circle rotations as topological factors. Given a homeomorphism of the $2$-torus without periodic points and exhibiting…
This article deals with directional rotational deviations for non-wandering periodic point free homeomorphisms of the 2-torus which are homotopic to the identity. We prove that under mild assumptions, such a homeomorphism exhibits uniformly…