Renormalization in one-dimensional dynamics

Motion of charged particles (78A35) Foliations in differential topology; geometric theory (57R30) Dynamical systems involving maps of the interval (37E05)

Cites Work

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Almost every interval translation map of three intervals is finite type
The quality of the diophantine approximations found by the Jacobi--Perron algorithm and related algorithms
Diffusion for chaotic plane sections of 3-periodic surfaces
Interval identification systems and plane sections of 3-periodic surfaces
Exponential mixing for the Teichmüller flow
A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces
Dynamical systems, topology, and conductivity in normal metals
Geometry of plane sections of the infinite regular skew polyhedron $\{4, 6 | 4\}$
A condition for minimal interval exchange maps to be uniquely ergodic
Interval exchange transformations and some special flows are not mixing
Gauss measures for transformations on the space of interval exchange maps
Interval exchange transformations and measured foliations
A 'minimal', non-uniquely ergodic interval exchange transformation
Non-ergodic interval exchange transformations
Dynamics for rotation pseudogroups
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Pseudogroups of isometries of $\mathbb{R}$ and Rips' theorem on free actions on $\mathbb{R}$-trees
Solutions of the cohomological equation for area-preserving flows on compact surfaces of higher genus
Connected components of the moduli spaces of Abelian differentials with prescribed singularities
Minimality of interval exchange transformations with restrictions
Invariant and stationary measures for the $\mathrm{SL}(2,\mathbb{R})$ action on moduli space
Stable actions of groups on real trees
Linearization of generalized interval exchange maps
On connectedness of chaotic sections of some 3-periodic surfaces
Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture
The Gauss map on a class of interval translation mappings
Ergodic theory of interval exchange maps
Asymptotic cycles
Double rotations
Weak mixing for interval exchange transformations and translation flows
Simplicity of spectra for certain multidimensional continued fraction algorithms
Minimal non uniquely ergodic IETs with flips
Symmetric band complexes of thin type and chaotic sections which are not quite chaotic
On the Hausdorff dimension of the Rauzy gasket
On typical leaves of a measured foliated 2-complex of thin type
Lower bounds on the dimension of the Rauzy gasket
The number of ergodic measures for transitive subshifts under the regular bispecial condition
Almost all interval exchange transformations with flips are nonergodic
The Hamiltonian formalism and a many-valued analogue of Morse theory
Simplicial systems for interval exchange maps and measured foliations
Représentation géométrique de suites de complexité $2n+1$
ON THE NUMBER OF INVARIANT MEASURES FOR FLOWS ON ORIENTABLE SURFACES
A problem of Novikov on the semiclassical motion of an electron in a uniform almost rational magnetic field
Deviation for interval exchange transformations
On the Hausdorff dimension of minimal interval exchange transformations with flips
Piecewise monotone maps without periodic points: rigidity, measures and complexity
Proof of S.P. Novikov's conjecture for the case of small perturbations of rational magnetic fields
Interval translation mappings
The Rauzy Gasket
Thermodynamic formalism for countable Markov shifts
Cohomological equations for linear involutions
A note on double rotations of infinite type
The cohomological equation for Roth-type interval exchange maps
Dynamics and geometry of the Rauzy–Veech induction for quadratic differentials
SELF-INVERSES, LAGRANGIAN PERMUTATIONS AND MINIMAL INTERVAL EXCHANGE TRANSFORMATIONS WITH MANY ERGODIC MEASURES
Minimality and the Rauzy – Veech algorithm for interval exchange transformations with flips
Weak mixing directions in non-arithmetic Veech surfaces
Dynamical Systems Around the Rauzy Gasket and Their Ergodic Properties
Interval exchange transformations
Dynamics of isometry systems: On the endpoints of orbits
Polygonal billiards with one sided scattering

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