Rotation numbers for quasiperiodically forced circle maps-mode-locking vs. strict monotonicity

DOI10.1090/S0894-0347-08-00627-9zbMath1206.37020arXivmath/0607598OpenAlexW1980936214MaRDI QIDQ3079200

Kristian Bjerklöv, Tobias Jäger

Publication date: 2 March 2011

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607598

zbMATH Keywords

rotation numbersmode-lockingquasiperiodically forced systems

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Topological dynamics of nonautonomous systems (37B55) Dynamical aspects of twist maps (37E40) Rotation numbers and vectors (37E45)

Related Items (12)

Almost periodic structures and the semiconjugacy problem ⋮ Resonance tongues in the quasi-periodic Hill-Schrödinger equation with three frequencies ⋮ Lower dimensional invariant tori for quasiperiodically forced circle diffeomorphisms ⋮ Linearization of quasiperiodically forced circle flows beyond Brjuno condition ⋮ Dynamics of the quasi-periodic Schrödinger cocycle at the lowest energy in the spectrum ⋮ Abundance of mode-locking for quasiperiodically forced circle maps ⋮ The rigidity of pseudo-rotations on the two-torus and a question of Norton-Sullivan ⋮ On topological genericity of the mode-locking phenomenon ⋮ Strange non-chaotic attractors in quasiperiodically forced circle maps ⋮ Strange non-chaotic attractors in quasi-periodically forced circle maps: Diophantine forcing ⋮ ρ-bounded orbits and Arnold tongues for quasiperiodically forced circle maps* ⋮ Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial-interglacial cycles

Cites Work

• Unnamed Item
• Unnamed Item
• The rotation number for finite difference operators and its properties
• Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2
• The rotation number for almost periodic potentials
• The structure of mode-locked regions in quasi-periodically forced circle maps
• On a Floquet theory for almost-periodic, two-dimensional linear systems
• Strange non-chaotic attractor in a quasiperiodically forced circle map
• Rotation numbers for quasi-periodically forced monotone circle maps
• Transitive sets for quasi-periodically forced monotone maps
• The Denjoy type of argument for quasiperiodically forced circle diffeomorphisms
• STRANGE NONCHAOTIC ATTRACTORS
• TOWARDS A CLASSIFICATION FOR QUASIPERIODICALLY FORCED CIRCLE HOMEOMORPHISMS
• Strict Ergodicity and Transformation of the Torus
• Positive Lyapunov exponent and minimality for a class of one-dimensional quasi-periodic Schrödinger equations

This page was built for publication: Rotation numbers for quasiperiodically forced circle maps-mode-locking vs. strict monotonicity