Related papers: Persistence of Heterodimensional Cycles
We consider Holder continuous linear cocycles over partially hyperbolic diffeomorphisms. For fiber bunched cocycles with one Lyapunov exponent we show continuity of measurable invariant conformal structures and sub-bundles. Further, we…
We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the…
We consider the dynamics of semiflows of patterns on unbounded domains that are equivariant under a noncompact group action. We exploit the unbounded nature of the domain in a setting where there is a strong `global' norm and a weak `local'…
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere $S^2$ is proved. A classification of these families up to moderate equivalence in neighborhoods of their large…
In this paper we analyze the heteroclinic cycle and the Hopf bifurcation of a generic dynamical system with the symmetry of the group $\mathbf{Q}_8,$ constructed via a Cayley graph. While the Hopf bifurcation is similar to that of a…
We study the spectral location of strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide"…
In this paper we study structurally stable homoclinic classes. In a natural way, the structural stability for an individual homoclinic class is defined through the continuation of periodic points. Since the homoclinic classes is not…
BPS monopoles which are periodic in one of the spatial directions correspond, via a generalized Nahm transform, to solutions of the Hitchin equations on a cylinder. A one-parameter family of solutions of these equations, representing a…
We consider a non-autonomous dynamical system formed by coupling two piecewise-smooth systems in $\RR^2$ through a non-autonomous periodic perturbation. We study the dynamics around one of the heteroclinic orbits of one of the…
We are interested in finding a dense part of the space of $C^1$-diffeomorphisms which decomposes into open subsets corresponding to different dynamical behaviors: we discuss results and questions in this direction. In particular we present…
We investigate the effect of a hyperbolic (or, more generally, isolated as an invariant set) closed Reeb orbit on the dynamics of a Reeb flow on the $(2n-1)$-dimensional standard contact sphere, extending two results previously known for…
A supersolid is a system that presents long-range order and shear rigidity as a solid but which also supports a non-dissipative superflow as a superfluid. From an effective perspective, supersolids are identified with phases of matter that…
Given a simply connected, closed four manifold, we associate to it a simply connected, closed, spin five manifold. This leads to several consequences : the stable and unstable homotopy groups of such a four manifold is determined by its…
We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the…
In this paper we study Holder continuous linear cocycles over transitive Anosov diffeomorphisms. Under various conditions of relative pinching we establish properties including existence and continuity of measurable invariant sub-bundles…
Stationary structures in a classical isotropic two-dimensional continuous Heisenberg ferromagnetic spin system are studied in the framework of the (2+1)-dimensional Landau-Lifshitz model. It is established that in the case of \vec S (\vec…
Persistent homology studies the birth and death of cycles in a parameterized family of spaces. In this paper, we study the birth and death of cycles in a multifiltration of a chain complex with the goal of producing a persistence diagram…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
In this work, we study the dynamics of piecewise smooth systems on a codimension-2 transverse intersection of two codimension-1 discontinuity sets. The Filippov convention can be extended to such intersections, but this approach does not…
Systems such as fluid flows in channels and pipes or the complex Ginzburg-Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial…