1 citations · 2 across the 13 of their papers we have counts for
18 papers
Numerical Computation of Quasiperiodic Reducible Saddle-Node Bifurcations: a Parameterization Method Approach
Jordi-Lluís Figueras, Joan Gimeno, Jeremy P. Parker
We present a method for computing reducible, normally hyperbolic, invariant tori with internal quasiperiodic dynamics in autonomous ordinary differential equation systems. The appr…
Extended Kalman Filtering on Stiefel Manifolds
Jordi-Lluís Figueras, Aron Persson, Lauri Viitasaari
A generalisation of the extended Kalman filter for Stiefel manifold-valued measurements is presented. We provide simulations on the 2-sphere and the space of orthogonal 4-by-2 matr…
On the Convergence of the Extended Kalman Filter on Stiefel Manifolds when Observing a Constant Particle with Measurement Errors
Jordi-Lluís Figueras, Aron Persson, Lauri Viitasaari
In this paper we first introduce the setting of filtering on Stiefel manifolds. Then, assuming the underlying system process is constant, the convergence of the extended Kalman fil…
Autoregressive Processes on Stiefel and Grassmann Manifolds
Jordi-Lluís Figueras, Aron Persson
System identification methods for autoregressive processes on Stiefel and Grassmann manifolds are presented and studied. We model the system parameters as elements of the orthogona…
On parameter estimation for based on projected data into
Jordi-Lluís Figueras, Aron Persson, Lauri Viitasaari
We consider the projected normal distribution, with isotropic variance, on the 2-sphere using intrinsic statistics. We show that in this case, the expectation commutes with the pro…
Computer Validation of Open Gaps for the Almost Mathieu Operator with Critical Coupling
Jordi-Lluís Figueras, Joaquim Puig
We present some computer assisted methods to prove the existence of spectral gaps for the Almost Mathieu operator at critical coupling and give rigorous numerical estimates on thei…
Self-Similar Singular Solutions to the Nonlinear Schrödinger and the Complex Ginzburg-Landau Equations
Joel Dahne, Jordi-Lluís Figueras
We prove the existence of radial self-similar singular solutions for the mass supercritical Nonlinear Schrödinger Equation far from the critical regime and, more generally, branche…
A parametrization algorithm to compute lower dimensional elliptic tori in Hamiltonian systems
Chiara Caracciolo, Jordi-Lluís Figueras, Alex Haro
We present an algorithm for the construction of lower dimensional elliptic tori in parametric Hamiltonian systems by means of the parametrization method with the tangent and normal…
Sun-Jupiter-Saturn System may exist: A verified computation of quasiperiodic solutions for the planar three body problem
Jordi-Lluís Figueras, Alex Haro
In this paper, we present evidence of the stability of a simplified model of the Solar System, a flat (Newtonian) Sun-Jupiter-Saturn system with realistic data: masses of the Sun a…
A Modified Parameterization Method for Invariant Lagrangian Tori for Partially Integrable Hamiltonian Systems
Jordi-Lluís Figueras, Alex Haro
In this paper we present an a-posteriori KAM theorem for the existence of an -parameters family of -dimensional isotropic invariant tori with Diophantine frequency vector…
The number of relative equilibria in the PCR4PB
Jordi-Lluís Figueras, Warwick Tucker, Piotr Zgliczynski
The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial…
Sharp -Hölder continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schrödinger cocycles
Jordi-Lluís Figueras, Thomas Ohlson Timoudas
We consider a similar type of scenario for the disappearance of uniform of hyperbolicity as in Bjerklöv and Saprykina (2008, Nonlinearity 21), where it was proved that the minimum…
Effective bounds for the measure of rotations
Jordi-Lluís Figueras, Alex Haro, Alejandro Luque
A fundamental question in Dynamical Systems is to identify regions of phase/parameter space satisfying a given property (stability, linearization, etc). Given a family of analytic…
On the sharpness of the Rüssmann estimates
Jordi-Lluís Figueras, Alex Haro, Alejandro Luque
Estimating the norm of the solution of the linear difference equation plays a fundamental role in KAM theory. Optimal (in certain sense) estimates for the soluti…
A Framework for the Numerical Computation and a Posteriori Verification of Invariant Objects of Evolution Equations
Jordi-Lluís Figueras, Marcio Gameiro, Jean Philippe Lessard +1
We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilib…
Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto-Sivashinsky Equation
Jordi-Lluís Figueras, Rafael de la Llave
We present numerical results and computer assisted proofs of the existence of periodic orbits for the Kuramoto-Sivashinky equation. These two results are based on writing down the…
Non-Smooth Bifurcations of Uniformly Hyperbolic Invariant Manifolds in Skew Product Systems: Rigorous Results
Jordi-Lluís Figueras, Dan Strängberg
In this paper we study the anti-integrable limit scenario of skew-product systems. We consider a generalization of such systems based on the Frenkel-Kontorova model, and prove the…
Rigorous computer assisted application of KAM theory: a modern approach
Jordi-Lluís Figueras, Alex Haro, Alejandro Luque
In this paper we present and illustrate a general methodology to apply KAM theory in particular problems, based on an {\em a posteriori} approach. We focus on the existence of real…