Related papers: Global bifurcations close to symmetry
A thorough analysis is performed to find traveling waves in a qualitative reaction-diffusion system inspired by a predator-prey model. We provide rigorous results coming from a standard local stability analysis, numerical bifurcation…
We derive the bifurcation set for a not previously considered three-parametric Bogdanov-Takens unfolding, showing that it is possible express its vector field as two different perturbed cubic Hamiltonians. By using several first-order…
We apply spatial dynamical-systems techniques to prove that certain spatiotemporal patterns in reversible reaction-diffusion equations undergo snaking bifurcations. That is, in a narrow region of parameter space, countably many branches of…
In this paper, we report the bifurcations of mode-locked periodic orbits occurring in maps of three or higher dimensions. The `torus' is represented by a closed loop in discrete time, which contains stable and unstable cycles of the same…
This thesis attempts to contribute to the study of differentiable dynamics both from a semi-local and global point of view. The center of study is differentiable dynamics in manifolds of dimension 3 where we are interested in the…
We prove that a "positive probability" subset of the boundary of the set of hyperbolic (Axiom A) surface diffeomorphisms with no cycles $\mathcal{H}$ is constituted by Kupka-Smale diffeomorphisms: all periodic points are hyperbolic and…
We construct open sets of degenerate unfoldings of heterodimensional cycles of any co-index $c>0$ and homoclinic tangencies of arbitrary codimension $c>0$. These sets are known to be the support of unexpected phenomena in families of…
We prove existence and uniqueness of equilibrium states for a family of partially hyperbolic systems, with respect to Holder continuous potentials with small variation. The family comes from the projection, on the center-unstable direction,…
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems…
We consider a heteroclinic network in the framework of winnerless competition of species. It consists of two levels of heteroclinic cycles. On the lower level, the heteroclinic cycle connects three saddles, each representing the survival of…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays…
A common external forcing can cause a saddle-node bifurcation in an ensemble of identical Duffing oscillators by breaking the symmetry of the individual bistable (double-well) unit. The strength of the forcing determines the separation…
We study a continuum Hatano--Nelson model with a saturating nonlinear nonreciprocity and analyze its stationary states via the associated phase-space flow. We uncover a global scenario controlled by a subcritical Hopf bifurcation and a…
New examples of harmonic unit vector fields on hyperbolic 3-space are constructed by exploiting the reduction of symmetry arising from the foliation by horospheres. This is compared and contrasted with the analogous construction in…
For every $k \geq 2$ and $n \geq 2$ we construct $n$ pairwise homotopically inequivalent simply-connected, closed $4k$-dimensional manifolds, all of which are stably diffeomorphic to one another. Each of these manifolds has hyperbolic…
Symmetry breaking phase transitions are an example of non-equilibrium processes that require real time treatment, a major challenge in strongly coupled systems without long-lived quasiparticles. Holographic duality provides such an approach…
State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses…
Heteroclinic cycles and networks are structures in dynamical systems composed of invariant sets and connecting heteroclinic orbits, and can be robust in systems with invariant subspaces. The usual method for analysing the stability of…
We study the relationship between homoclinic orbits associated to repellors, usually called snap-back repellors, and expanding sets of smooth endomorphisms. Critical homoclinic orbits constitutes an interesting bifurcation that is locally…