The bitransitive continuous maps of the interval are conjugate to maps extremely chaotic a. e.
The bounce problem, on n-dimensional Riemannian manifolds
In questo lavoro vengono generalizzati i risultati relativi al problema del rimbalzo unidimensionale studiato in [5]. Precisamente si considera un punto mobile su una varietà Riemanniana -dimensionale, soggetto all’azione di un potenziale variabile nel tempo e vincolato a restare in una parte di avente un bordo di classe contro cui il punto «rimbalza»....
The branch locus for one-dimensional Pisot tiling spaces
If φ is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Φ on the tiling space factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Φ-periodic asymptotic tilings corresponds to a finite set that projects onto the branch locus in a d-torus. We prove that if two such tiling spaces are homeomorphic, then the resulting branch loci are the same up to the action of certain affine maps on the torus.
The C 1 generic diffeomorphism has trivial centralizer
Answering a question of Smale, we prove that the space of C 1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
The interior of zero entropy diffeomorphisms.
The invariance of the algebraic multiplicity of a holomorphic vector field
We prove that the algebraic multiplicity of a holomorphic vector field at an isolated singularity is invariant by equivalences.
The hypothesis in Pesin theory
The canonical structure of the supersymmetric non-linear σ model in the constrained hamiltonian formalism
The capacity of parabolic Julia sets.
The Cauchy problem for the Gross–Pitaevskii equation
The centralizer of Morse shifts
The centralizer of Morse shifts induced by arbitrary blocks
The chain recurrent set for maps of compacta
For a self-map of a compactum we give a necessary and sufficient condition for the chain recurrent set to be precisely the set of periodic points.
The characteristic variety of a generic foliation
We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.
The Circle Problem on Surfaces of Variable Negative Curvature.
The classification of circle-like continua that admit expansive homeomorphisms
A homeomorphism h: X → X of a compactum X is expansive provided that for some fixed c > 0 and every x, y ∈ X (x ≠ y) there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(y)) > c. It is shown that if X is a solenoid that admits an expansive homeomorphism, then X is homeomorphic to a regular solenoid. It can then be concluded that a circle-like continuum admits an expansive homeomorphism if and only if it is homeomorphic to a regular solenoid.
The classification of tiling space flows.
The coexistence problem" for conservative dynamical systems: a review
The cohomological equation for area-preserving flows on compact surfaces.
The compact category and mulitple periodic solutions of Hamiltionian systems on symmetric starshaped energy surfaces.