Limit set
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Spectral gaps without the pressure condition Open
For all convex co-compact hyperbolic surfaces, we prove the existence of an\nessential spectral gap, that is a strip beyond the unitarity axis in which the\nSelberg zeta function has only finitely many zeroes. We make no assumption on\nthe…
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Phase-sensitivity bounds for two-mode interferometers Open
We provide general bounds of phase estimation sensitivity in linear two-mode\ninterferometers. We consider probe states with a fluctuating total number of\nparticles. With incoherent mixtures of state with different total number of\npartic…
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Kosambi–Cartan–Chern (KCC) theory for higher-order dynamical systems Open
The Kosambi–Cartan–Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric description of the time evolution of a dynamical system, wi…
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Weak separation condition, Assouad dimension, and Furstenberg homogeneity Open
We consider dimensional properties of limit sets of Moran constructions\nsatisfying the finite clustering property. Just to name a few, such limit sets\ninclude self-conformal sets satisfying the weak separation condition and\ncertain sub-…
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On the random dynamics of Volterra quadratic operators Open
We consider random dynamical systems generated by a special class of Volterra quadratic stochastic operators on the simplex $S^{m-1}$ . We prove that in contrast to the deterministic set-up the trajectories of the random dynamical system a…
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Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems Open
We show that for systems that allow a Young tower construction with polynomiallydecaying correlations the return times to metric balls are in the limit Poisson distributed.We also provide error terms which are powers of logarithm of the ra…
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Global dynamics of SVIR epidemic model with distributed delay and imperfect vaccine Open
In this research, we investigate an SVIR system with distributed delay. We first provide some preliminary results on the proprieties of the Volterra function and the well-posedness of the solution, also the existence of a global compact at…
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Non-autonomous dynamical systems Open
This review paper treats the dynamics of non-autonomous dynamical systems. To study the forwards asymptotic behaviour of a non-autonomous differential equation we need to analyse the asymptotic configurations of the non-autonomous terms pr…
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On Rough ℐ<sub>2</sub>-Convergence of Double Sequences Open
In this study, we introduce the notion of rough ℐ_2-convergence and the set of rough ℐ_2-limit points of a double sequence and obtained two rough ℐ_2-convergence criteria associated with this set. Later, we proved that this set is closed a…
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On rough convergence in 2-normed spaces and some properties Open
In this study, we investigated relationships between rough convergence and classical convergence and studied some properties about the notion of rough convergence, the set of rough limit points and rough cluster points of a sequence in 2-n…
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ON A PLANAR DYNAMICAL SYSTEM ARISING IN THE NETWORK CONTROL THEORY Open
We study the structure of attractors in the two-dimensional dynamical system that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive paramet…
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Anosov representations with Lipschitz limit set Open
We study Anosov representations whose limit set has intermediate regularity,\nnamely is a Lipschitz submanifold of a flag manifold. We introduce an explicit\nlinear functional, the unstable Jacobian, whose orbit growth rate is integral\non…
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Hopf Bifurcations in Complex Multiagent Activity: The Signature of Discrete to Rhythmic Behavioral Transitions Open
Most human actions are composed of two fundamental movement types, discrete and rhythmic movements. These movement types, or primitives, are analogous to the two elemental behaviors of nonlinear dynamical systems, namely, fixed-point and l…
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Lyapunov Stability and Attraction Under Equivariant Maps Open
Let M and N be admissible Hausdorff topological spaces endowed with admissible families of open coverings. Assume that is a semigroup acting on both M and N . In this paper we study the behavior of limit sets, prolongations, prolongational…
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Multifractal analysis of the irregular set for almost-additive sequences via large deviations Open
In this paper we introduce a notion of free energy and large deviations rate\nfunction for asymptotically additive sequences of potentials via an\napproximation method by families of continuous potentials. We provide estimates\nfor the top…
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Emergent space-time via a geometric renormalization method Open
We present a purely geometric renormalization scheme for metric spaces\n(including uncolored graphs), which consists of a coarse graining and a\nrescaling operation on such spaces. The coarse graining is based on the concept\nof quasi-isom…
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Intermediate dimensions of infinitely generated attractors Open
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of contractions. Our primary focus is on the intermediate dimensions: a family of dimensions depending on a parameter which…
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Different Statistical Future of Dynamical Orbits over Expanding or Hyperbolic Systems (I): Empty Syndetic Center Open
In the theory of dynamical systems, a fundamental problem is to study the asymptotic behavior of dynamical orbits. Lots of different asymptotic behavior have been learned including different periodic-like recurrence such periodic and almos…
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Attractors for Multivalued Impulsive Systems: Existence and Applications to Reaction-Diffusion System Open
In this paper, we develop a general approach to investigate limit dynamics of infinite-dimensional dissipative impulsive systems whose initial conditions do not uniquely determine their long time behavior. Based on the notion of an uniform…
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Asymptotic invariance and the discretisation of nonautonomous forward attracting sets Open
The $\omega$-limit set $\omega_B$ of a nonautonomous dynamical system generated by a nonautonomous ODE with a positive invariant compact absorbing set $B$ is shown to be asymptotic positive invariant in general and asymptotic negative inva…
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Entropy, minimal surfaces and negatively curved manifolds Open
Taubes [Minimal surfaces in germs of hyperbolic 3-manifolds. Proceedings of the Casson Fest, Geom. Topol. Monogr. 7 (2004), 69–100 (electronic)] introduced the space of minimal hyperbolic germs with elements consisting of the first and sec…
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Pushing the limit of quantum transport simulations Open
International audience
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Invariance of Ideal Limit Points Open
Let I be an analytic P-ideal [respectively, a summable ideal] on the positive integers and let (xn) be a sequence taking values in a metric space X. First, it is shown that the set of ideal limit points of (xn) is an Fσ-set [resp., a close…
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Critical Exponent and Hausdorff Dimension in Pseudo-Riemannian Hyperbolic Geometry Open
The aim of this article is to understand the geometry of limit sets in pseudo-Riemannian hyperbolic geometry. We focus on a class of subgroups of $\textrm{PO}(p,q+1)$ introduced by Danciger, Guéritaud, and Kassel, called ${\mathbb{H}}^{p,q…
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Limit sets of Teichmüller geodesics with minimal nonuniquely ergodic vertical foliation, II Open
Given a sequence of curves on a surface, we provide conditions which ensure that (1) the sequence is an infinite quasi-geodesic in the curve complex, (2) the limit in the Gromov boundary is represented by a nonuniquely ergodic ending lamin…
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The Central Limit Theorem for Random Dynamical Systems Open
We consider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. The Central Limit Theorem for random dynamical systems is established.
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Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation Open
We describe a method for constructing Teichmüller geodesics where the vertical foliation ν is minimal but is not uniquely ergodic and where we have a good understanding of the behavior of the Teichmüller geodesic. The construction depends …
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Compact attractors of an antithetic integral feedback system have a simple structure Open
Since its introduction by Briat, Gupta and Khammash, the antithetic feedback controller design has attracted considerable attention in both theoretical and experimental systems biology. The case in which the plant is a two-dimensional line…
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Persistence of Excitation in Reproducing Kernel Hilbert Spaces, Positive Limit Sets, and Smooth Manifolds Open
This paper studies the relationship between the positive limit sets of continuous semiflows and the newly introduced definition of persistently excited (PE) sets and associated subspaces of reproducing kernel Hilbert (RKH) spaces. It is sh…
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On the limit set of root systems of Coxeter groups acting on Lorentzian spaces Open
The notion of limit roots of a Coxeter group W was recently introduced (see arXiv:1112.5415 and arXiv:1303.6710): they are the accumulation points of directions of roots of a root system for W. In the case where the root system lives in a …