4 citations · 23 across the 17 of their papers we have counts for
21 papers
Stable manifolds of heteroclinic chains in Hořava-Lifshitz cosmology
Hauke Sprink, Phillipo Lappicy
We consider vacuum spatially homogeneous models in Hořava-Lifshitz gravity, which are expected to describe generic singularities for these modified gravity theories. These models p…
The Bianchi IX Attractor in Modified Gravity
Ester Beatriz, Everaldo Bonotto, Phillipo Lappicy
We consider vacuum anisotropic spatially homogeneous models in certain modified gravity theories (such as Hořava-Lifshitz, - or gravity), which are expected to describ…
A Practical Guide to Rigorously Locate Periodic Orbits in Discrete Dynamics
Lucía Alonso Mozo, Olivier Hénot, Phillipo Lappicy
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to…
Global Continuation of Stable Periodic Orbits in Systems of Competing Predators
Kevin E. M. Church, Jia-Yuan Dai, Olivier Hénot +2
We develop a continuation technique to obtain global families of stable periodic orbits, delimited by transcritical bifurcations at both ends. To this end, we formulate a zero-find…
On bifurcation from infinity: a compactification approach
José M. Arrieta, Juliana Fernandes, Phillipo Lappicy
We consider a scalar parabolic partial differential equation on the interval with nonlinear boundary conditions that are asymptotically sublinear. As the parameter crosses critical…
Oscillatory spacelike singularities: The Bianchi type vacuum models
Phillipo Lappicy, Claes Uggla
The Bianchi type , and vacuum models all have 4-dimensional Hubble-normalized state spaces and are expected to have a generic init…
Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria
Alejandro López-Nieto, Phillipo Lappicy, Nicola Vassena +2
We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations: Such bifurcations occur when a…
Periodic orbits in Hořava-Lifshitz cosmologies
Kevin E. M. Church, Olivier Hénot, Phillipo Lappicy +2
We consider spatially homogeneous Hořava-Lifshitz (HL) models that perturb General Relativity (GR) by a parameter such that GR occurs at . We describe the dynam…
An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension
Phillipo Lappicy, Ester Beatriz
Energy (or Lyapunov) functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Matano constructed a Lyapunov function for…
Chaos in spatially homogeneous Hořava-Lifshitz subcritical cosmologies
Phillipo Lappicy, Victor H. Daniel
We consider spatially homogeneous models in Hořava-Lifshitz (HL) gravity that perturbs General Relativity (GR) by a parameter such that GR occurs at . We prove…
A Unified Theory for Inertial Manifolds, Saddle Point Property and Exponential Dichotomy
Alexandre N. Carvalho, Phillipo Lappicy, Estefani M. Moreira +1
Inertial manifold theory, saddle point property and exponential dichotomy have been treated as different topics in the literature with different proofs. As a common feature, they a…
Sturm attractors for fully nonlinear parabolic equations
Phillipo Lappicy
We explicitly construct global attractors of fully nonlinear parabolic equations. The attractors are decomposed as equilibria (time independent solutions) and heteroclinic orbits (…
Bifurcations and Chaos in Hořava-Lifshitz Cosmology
Juliette Hell, Phillipo Lappicy, Claes Uggla
The nature of generic spacelike singularities in general relativity is connected with first principles, notably Lorentzian causal structure, scale invariance and general covariance…
A symmetry property for elliptic equations on the sphere
Phillipo Lappicy
The goal of this paper is to study how the symmetry of the spherical domain influences solutions of elliptic equations on such domain. The method pursued is a variant of the moving…
Ginzburg-Landau patterns in circular and spherical geometries: vortices, spirals and attractors
Jia-Yuan Dai, Phillipo Lappicy
This paper consists of three results on pattern formation of Ginzburg-Landau -armed vortex solutions and spiral waves in circular and spherical geometries. First, we completely…
Conley's index and connection matrices for non-experts
Phillipo Lappicy
This is a self-contained tour of the Conley index and connection matrices. The starting point is Conley's fundamental theorem of dynamical systems. There is a short stop at the nec…
Unbounded Sturm attractors for quasilinear equations
Phillipo Lappicy, Juliana Fernandes Pimentel
We analyze the asymptotic dynamics of quasilinear parabolic equations when solutions may grow up (i.e., blow up in infinite time). For such models, there is a global attractor whic…
Space of initial data for self-similar Schwarzschild solutions
Phillipo Lappicy
The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the…
Sturm attractors for quasilinear parabolic equations
Phillipo Lappicy
The goal of this paper is to construct explicitly the global attractors of quasilinear parabolic equations, as it was done for the semilinear case by Brunovský and Fiedler (1986),…
Sturm attractors for quasilinear parabolic equations with singular coefficients
Phillipo Lappicy
The goal of this paper is to construct explicitly the global attractors of parabolic equations with singular diffusion coefficients on the boundary, as it was done without the sing…
A Lyapunov function for fully nonlinear parabolic equations in one spatial variable
Phillipo Lappicy, Bernold Fiedler
Lyapunov functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Zelenyak (1968) and Matano (1988) constructed a Lyapun…