34 citations · 73 across the 20 of their papers we have counts for
24 papers
The reverse Ritz inclusion: computable bounds on the pseudospectra of an operator by those of a finite-rank compression
Isaia Nisoli
We consider a bounded operator on a separable complex Hilbert space, reached only through its action on vectors and that of its adjoint, and split it along a subspace of finite dim…
(co)Quasi-irreducible and (co)expanding random maps
Pablo G. Barrientos, Isaia Nisoli, Dominique Malicet
We study quasi-irreducibility, expansion, and their cotangent duals for random (local) diffeomorphisms on compact invariant sets of a Riemannian manifold. Quasi-irreducibilit…
Statistical periodicity in noise-induced order from Ruelle-Pollicott resonances
Yuzuru Sato, Isaia Nisoli
Noise-induced order (NIO) is a paradigmatic example of nontrivial noise-induced phenomena, characterized by pronounced spectral peaks and pseudoperiodic dynamics. We show that this…
Ulam Approximation for Nonautonomous Systems: Equivariant Measures and Linear Response
Stefano Galatolo, Valerio Lucarini, Isaia Nisoli
Despite the prevalence of nonautonomous systems in applications, their statistical properties are much less understood than in the autonomous setting. Building on recent results on…
Integral representation of Lyapunov exponents
Pablo G. Barrientos, Isaia Nisoli
We introduce a new operator-theoretic construction of Lyapunov growth for Markov-driven systems. The construction is based on an abstract variational principle for asymptotic growt…
Certified spectral approximation of transfer operators and the Gauss map
Isaia Nisoli
We prove that the full spectral picture of a transfer operator (every isolated eigenvalue, eigenvector, and Riesz projector outside the essential spectral radius) can be approximat…
Efficient computation of stationary measures and the Lyapunov Landscape for families random dynamical systems with smooth additive noise
Stefano Galatolo, Charles Lopez Vereau, Luigi Marangio +1
We present an efficient and validated method for approximating the stationary measures of random dynamical systems with smooth additive noise. The approach leverages the strong reg…
A pseudospectral approach to rigorous numerical estimation of resonances of transfer operators
Alex Blumenthal, Isaia Nisoli, Toby Taylor-Crush
{Ruelle-Pollicott} resonances, isolated eigenvalues of a transfer operator acting on suitably chosen Banach spaces, play a fundamental role in understanding the statistical propert…
Designing robust trajectories by lobe dynamics in low-dimensional Hamiltonian systems
Naoki Hiraiwa, Mai Bando, Isaia Nisoli +1
Modern space missions with uncrewed spacecraft require robust trajectory design to connect multiple chaotic orbits by small controls. To address this issue, we propose a control sc…
A general framework for the rigorous computation of invariant densities and the coarse-fine strategy
Stefano Galatolo, Maurizio Monge, Isaia Nisoli +1
In this paper we present a general, axiomatical framework for the rigorous approximation of invariant densities and other important statistical features of dynamics. We approximate…
Rigorous Computation of Linear Response for Intermittent Maps
Isaia Nisoli, Toby Taylor-Crush
We present a rigorous numerical scheme for the approximation of the linear response of the invariant density of a map with an indifferent fixed point, with explicit and computed es…
Noise induced order for skew-products over a non-uniformly expanding base
Alex Blumenthal, Isaia Nisoli
Noise-induced order is the phenomenon by which the chaotic regime of a deterministic system is destroyed in the presence of noise. In this manuscript, we establish noise-induced or…
Existence of multiple noise-induced transitions in a Lasota-Mackey map
Takumi Chihara, Yuzuru Sato, Isaia Nisoli +1
We prove the existence of multiple noise-induced transitions in the Lasota-Mackey map, which is a class of one dimensional random dynamical system with additive noise. The result i…
How does noise induce order?
Isaia Nisoli
In this paper we present a general result with an easily checkable condition that ensures a transition from chaotic regime to regular regime in random dynamical systems with additi…
Existence of Noise Induced Order, a Computer Aided Proof
Stefano Galatolo, Maurizio Monge, Isaia Nisoli
We prove the existence of Noise Induced Order in the Matsumoto-Tsuda model, where it was originally discovered in 1983 by numerical simulations. This is a model of the famous Belos…
Decay of correlations, quantitative recurrence and logarithm law for contracting Lorenz attractors
Stefano Galatolo, Isaia Nisoli, Maria José Pacifico
In this paper we prove that a class of skew products maps with non uniformly hyperbolic base has exponential decay of correlations. We apply this to obtain a logarithm law for the…
A Rigorous Computational Approach to Linear Response
Wael Bahsoun, Stefano Galatolo, Isaia Nisoli +1
We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an…
Towards a Morse theory on Banach spaces via ultrafunctions
Vieri Benci, Isaia Nisoli
Morse Theory on Banach spaces would be a useful tool in nonlinear analysis but its development is hindered by many technical problems. In this paper we present an approach based on…
Rigorous approximation of diffusion coefficients for expanding maps
Wael Bahsoun, Stefano Galatolo, Isaia Nisoli +1
We use Ulam's method to provide rigorous approximation of diffusion coefficients for uniformly expanding maps. An algorithm is provided and its implementation is illustrated using…
An elementary way to rigorously estimate convergence to equilibrium and escape rates
Stefano Galatolo, Isaia Nisoli, Benoît Saussol
We show an elementary method to have (finite time and asymptotic) computer assisted explicit upper bounds on convergence to equilibrium (decay of correlations) and escape rate for…
Rigorous computation of invariant measures and fractal dimension for piecewise hyperbolic maps: 2D Lorenz like maps
Stefano Galatolo, Isaia Nisoli
We consider a class of piecewise hyperbolic maps from the unit square to itself preserving a contracting foliation and inducing a piecewise expanding quotient map, with infinite de…
An elementary approach to rigorous approximation of invariant measures
Stefano Galatolo, Isaia Nisoli
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of…
Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds
Stefano Galatolo, Isaia Nisoli
We show that in a rapidly mixing flow with an invariant measure, the time which is needed to hit a given section is related to a sort of conditional dimension of the measure at the…
Partial holomorphic connections and extension of foliations
Isaia Nisoli
This paper stresses the strong link between the existence of partial holomorphic connections on the normal bundle of a foliation seen as a quotient of the ambient tangent bundle an…