-smoothness of invariant fiber bundles for dynamic equations on measure chains.
4 Feuilletages et mécanique hamiltonienne
A Brouwer-like theorem for orientation reversing homeomorphisms of the sphere
We provide a topological proof that each orientation reversing homeomorphism of the 2-sphere which has a point of period k ≥ 3 also has a point of period 2. Moreover if such a k-periodic point can be chosen arbitrarily close to an isolated fixed point o then the same is true for the 2-periodic point. We also strengthen this result by proving that if an orientation reversing homeomorphism h of the sphere has no 2-periodic point then the complement of the fixed point set can be covered by invariant...
A class of strongly cooperative systems without compactness
A Closing Lemma on the Interval.
A concentration Phenomenon in Mean curvature Flow.
A continuity property of the dimension of the harmonic measure of Cantor sets under perturbations
A counterexample to a Fedorenko statement.
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas
We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.
A dimension group for local homeomorphisms and endomorphisms of onesided shifts fo finite type.
A fixed point theorem for branched covering maps of the plane
It is known that every homeomorphism of the plane which admits an invariant non-separating continuum has a fixed point in the continuum. In this paper we show that any branched covering map of the plane of degree d, |d| ≤ 2, which has an invariant, non-separating continuum Y, either has a fixed point in Y, or is such that Y contains a minimal (in the sense of inclusion among invariant continua), fully invariant, non-separating subcontinuum X. In the latter case, f has to be of degree -2 and X has...
A Foliated Metric Rigidity Theorem for Higher Rank Irreducible Symmetric Spaces.
A global perspective for non-conservative dynamics
A gradient inequality at infinity for tame functions.
Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.
A Horseshoe with Positive Measure.
A hybrid domain analysis for systems with delays in state and control.
A joint limit theorem for compactly regenerative ergodic transformations
We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zₙ,Sₙ), where Zₙ and Sₙ are respectively the time of the last visit before time n to, and the occupation time of, a suitable set Y of finite measure.
A KAM theorem for infinite-dimensional discrete systems.
A KAM-theorem for some nonlinear partial differential equations
A lemma and a conjecture on the cost of rearrangements