Nonlinear time series: computations and applications.
Nonlinear vibrations of completely resonant wave equations
We present recent existence results of small amplitude periodic and quasi-periodic solutions of completely resonant nonlinear wave equations. Both infinite-dimensional bifurcation phenomena and small divisors difficulties occur. The proofs rely on bifurcation theory, Nash-Moser implicit function theorems, dynamical systems techniques and variational methods.
Nonlinear vibrations, stability analysis, and control.
Nonlinearity in social dynamics -- order versus chaos.
Non-orbit equivalent actions of
For any , we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group . These actions arise as diagonal products between a generalized Bernoulli action and the action , where is seen as a subgroup of .
Non-recurrent meromorphic functions
We consider a transcendental meromorphic function f belonging to the class ℬ (with bounded set of singular values). We show that if the Julia set J(f) is the whole complex plane ℂ, and the closure of the postcritical set P(f) is contained in B(0,R) ∪ {∞} and is disjoint from the set Crit(f) of critical points, then every compact and forward invariant set is hyperbolic, provided that it is disjoint from Crit(f). It is further shown, under general additional hypotheses, that f admits no measurable...
Nonseparated manifolds and completely unstable flows.
Nonsingular cocycles and piecewise linear time changes.
Non-smooth variational bifurcation
We consider bifurcation problems associated with some lower semicontinuous functionals that do not satisfy the usual regularity assumptions. For such functionals it is possible to define a generalized "Hessian form" and to show that certain eigenvalues of this one are bifurcation values. The results are applied to a bifurcation problem for elliptic variational inequalities.
Non-standard dynamical systems. Shadows of trajectories and abstracts rivers.
Nonstandard numerical methods for a class of predator-prey models with predator interference.
Nonstationary normal forms and rigidity of group actions.
Non-transitive points and porosity
We establish that for a fairly general class of topologically transitive dynamical systems, the set of non-transitive points is very small when the rate of transitivity is very high. The notion of smallness that we consider here is that of σ-porosity, and in particular we show that the set of non-transitive points is σ-porous for any subshift that is a factor of a transitive subshift of finite type, and for the tent map of [0,1]. The result extends to some finite-to-one factor systems. We also show...
Nontrivial periodic solutions for strong resonance hamiltonian systems
Nontrivial periodic solutions of asymptotically linear Hamiltonian systems.
Non-Typical Points for β-Shifts
We study sets of non-typical points under the map mod 1 for non-integer β and extend our results from [Fund. Math. 209 (2010)] in several directions. In particular, we prove that sets of points whose forward orbit avoid certain Cantor sets, and the set of points for which ergodic averages diverge, have large intersection properties. We observe that the technical condition β > 1.541 found in the above paper can be removed.
Nonuniform center bunching and the genericity of ergodicity among partially hyperbolic symplectomorphisms
We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns–Wilkinson and Avila–Santamaria–Viana. Combining this new technique with other constructions we prove that -generic partially hyperbolic symplectomorphisms are ergodic. We also construct new examples of stably ergodic partially hyperbolic diffeomorphisms.
Non-uniformly expanding dynamics in maps with singularities and criticalities
Non-uniformly hyperbolic billiards
Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles
In the present paper, we advance considerably the current knowledge on the topic of bifurcations of heteroclinic cycles for smooth, meaning C ∞, parametrized families {g t ∣t∈ℝ} of surface diffeomorphisms. We assume that a quadratic tangency q is formed at t=0 between the stable and unstable lines of two periodic points, not belonging to the same orbit, of a (uniformly hyperbolic) horseshoe K (see an example at the Introduction) and that such lines cross each other with positive relative speed as...