34 citations · 146 across the 16 of their papers we have counts for
17 papers
On an Analytical Criterion for Detecting Intermittent Turbulent Behaviour of Solutions of Partial Differential Equations
Michele V Bartuccelli, Guido Gentile
A main question in the study of partial differential equations is the following: how do we understand the nature of the solutions and, in particular, how do we determine if a given…
Pseudo-synchronous solutions for dissipative non-autonomous systems
Michele Bartuccelli, Livia Corsi, Jonathan Deane +1
In the framework of KAM theory, the persistence of invariant tori in quasi-integrable systems is proved by assuming a non-resonance condition on the frequencies, such as the standa…
Periodic and quasi-periodic attractors for the spin-orbit evolution of Mercury with a realistic tidal torque
Michele Bartuccelli, Jonathan Deane, Guido Gentile
Mercury is entrapped in a 3:2 resonance: it rotates on its axis three times for every two revolutions it makes around the Sun. It is generally accepted that this is due to the larg…
Explicit estimates on the torus for the sup-norm and the crest factor of solutions of the Modified Kuramoto-Sivashinky Equation in one and two space dimensions
Michele V. Bartuccelli, Jonathan H. Deane, Guido Gentile
We consider the Modified Kuramoto-Sivashinky Equation (MKSE) in one and two space dimensions and we obtain explicit and accurate estimates of various Sobolev norms of the solutions…
Numerics for the spin orbit equation of Makarov with constant eccentricity
Michele V. Bartuccelli, Jonathan H. B. Deane, Guido Gentile
We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is in the velocity. Such an ODE arises as a model of spi…
Stable dynamics in forced systems with sufficiently high/low forcing frequency
M. Bartuccelli, G. Gentile, J. A. Wright
We consider a class of parametrically forced Hamiltonian systems with one-and-a-half degrees of freedom and study the stability of the dynamics when the frequency of the forcing is…
The high-order Euler method and the spin-orbit model A fast algorithm for solving differential equations with small, smooth nonlinearity
Michele V. Bartuccelli, Jonathan H. B. Deane, Guido Gentile
We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small diss…
Basins of attraction in forced systems with time-varying dissipation
James A. Wright, Jonathan H. B. Deane, Michele Bartuccelli +1
We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipa…
The effects of time-dependent dissipation on the basins of attraction for the pendulum with oscillating support
James A. Wright, Michele Bartuccelli, Guido Gentile
We consider a pendulum with vertically oscillating support and time-dependent damping coefficient which varies until reaching a finite final value. The sizes of the corresponding b…
Attractiveness of periodic orbits in parametrically forced systemswith time-increasing friction
Michele Bartuccelli, Jonathan Deane, Guido Gentile
We consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly…
Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus
Michele V. Bartuccelli, Jonathan H. B. Deane, Sergey Zelik
We give a comprehensive study of interpolation inequalities for periodic functions with zero mean, including the existence of and the asymptotic expansions for the extremals, best…
Arnold tongues for a resonant injection-locked frequency divider: analytical and numerical results
Michele V. Bartuccelli, Jonathan H. B. Deane, Guido Gentile +1
In this paper we consider a resonant injection-locked frequency divider which is of interest in electronics, and we investigate the frequency locking phenomenon when varying the am…
Frequency locking in the injection-locked frequency divider equation
Michele V. Bartuccelli, Jonathan H. B. Deane, Guido Gentile
We consider a model for the injection-locked frequency divider, and study analytically the locking onto rational multiples of the driving frequency. We provide explicit formulae fo…
Quasi-periodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
Guido Gentile, Michele V. Bartuccelli, Jonathan H. B. Deane
We consider a class of ordinary differential equations describing one-dimensional analytic systems with a quasi-periodic forcing term and in the presence of damping. In the limit o…
Bifurcation curves of subharmonic solutions
Guido Gentile, Michele V. Bartuccelli, Jonathan H. B. Deane
We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, w…
Globally and locally attractive solutions for quasi-periodically forced systems
Michele V. Bartuccelli, Jonathan H. B. Deane, Guido Gentile
We consider a class of differential equations, , with , describing one-dimensional dissipative systems subject to a periodic or…
Summation of divergent series and Borel summability for strongly dissipative equations with periodic or quasi-periodic forcing terms
Guido Gentile, Michele V. Bartuccelli, Jonathan H. B. Deane
We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasi-periodic analytic forcing term and in the presence of damping. A…