Trace maps as 3D reversible dynamical systems with an invariant

DOI10.1007/BF02188581zbMath0830.58025MaRDI QIDQ1896799

Michael Baake, John A. G. Roberts

Publication date: 22 October 1995

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

dynamical systemsreversible systemsquasicrystalsorbit analysissubstitution rulesperiod doublingtrace mapspseudo-Anosov systems

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems with hyperbolic behavior (37D99)

Related Items (20)

Reversing \(k\)-symmetries in dynamical systems ⋮ Local bifurcations on the plane with reversing point group symmetry ⋮ Nonperiodic Ising quantum chains and conformal invariance ⋮ Reversing and extended symmetries of shift spaces ⋮ Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients. I: The essential support of the measure ⋮ Properties of 1D classical and quantum Ising models: rigorous results ⋮ On the spectrum of 1D quantum Ising quasicrystal ⋮ Resonant driving and \(k\)-symmetry ⋮ KAM-stable Hamiltonians ⋮ Volume-preserving maps with an invariant ⋮ Continuum Schrödinger operators associated with aperiodic subshifts ⋮ 𝐶*-algebras of homoclinic and heteroclinic structure in expansive dynamics ⋮ Periodic orbits in \(k\)-symmetric dynamical systems ⋮ A new method to compute periodic orbits in general symplectic maps ⋮ The Fibonacci Hamiltonian ⋮ The structure of reversing symmetry groups ⋮ Self-similarity of Period-doubling Branching in 3-D Reversible Mappings ⋮ Curves of period two points for trace maps ⋮ Substitution Hamiltonians with bounded trace map orbits ⋮ Trace identities from identities for determinants

Cites Work

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• Symbolic dynamics for the renormalization map of a quasiperiodic Schrödinger equation
• Reversible systems
• Rings of Fricke characters and automorphism groups of free groups
• Stabilité et conjugaison différentiable pour certains feuilletages
• On the trace map for products of matrices associated with substitutive sequences
• Singularities and groups in bifurcation theory. Volume II
• Spectral properties of one dimensional quasi-crystals
• Nonperiodic Ising quantum chains and conformal invariance
• ELECTRONIC STATES OF QUASIPERIODIC SYSTEMS: FIBONACCI AND PENROSE LATTICES
• On the geometry and dynamics of diffeomorphisms of surfaces
• Reversing symmetries in dynamical systems
• TRACE MAPS, INVARIANTS, AND SOME OF THEIR APPLICATIONS
• Fricke-Klein geometry for the group Sl(2,C)
• Characters of free groups represented in the two‐dimensional special linear group
• Pseudo-Anosov homeomorphisms on a sphere with four punctures have all periods
• The nature of the atomic surfaces of quasiperiodic self-similar structures
• Trace maps for arbitrary substitution sequences

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