Some flesh on the skeleton: the bifurcation structure of bimodal maps
From MaRDI portal
Publication:580805
DOI10.1016/0167-2789(87)90040-6zbMath0626.58038OpenAlexW2163891442MaRDI QIDQ580805
Charles Tresser, Robert S. MacKay
Publication date: 1987
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0167-2789(87)90040-6
Applications of global analysis to the sciences (58Z05) Iteration of real functions in one variable (26A18) Local and nonlocal bifurcation theory for dynamical systems (37G99)
Related Items
Bifurcations in a Periodically Stimulated Limit Cycle Oscillator with Finite Relaxation Times ⋮ Transition to topological chaos for circle maps ⋮ Adaptive decision dynamics: bifurcations, multistability and chaos ⋮ Symmetries of star products and metric universalities in 1D quadri-modal maps ⋮ Metric universalities and systems of renormalization group equations for bimodal maps ⋮ Piecewise linear models for the quasiperiodic transition to chaos ⋮ Kneading plane of the circle map ⋮ Logistic-like and Gauss coupled maps: the born of period-adding cascades ⋮ Universal scaling of rotation intervals for quasi-periodically forced circle maps ⋮ Essential dynamics for Lorenz maps on the real line and the lexicographical world ⋮ Nonlinear three-wave interaction with non-conservative coupling ⋮ Dynamics in a nonlinear Keynesian good market model ⋮ Bifurcations of 2-Periodic Nonautonomous Stunted Tent Systems ⋮ Connecting Anti-integrability to Attractors for Three-Dimensional Quadratic Diffeomorphisms ⋮ New universal bifurcation scenario in one-dimensional trimodal maps ⋮ Devil's carpet of topological entropy and complexity of global dynamical behavior ⋮ From bimodal one-dimensional maps to Hénon-like two-dimensional maps: does quantitative universality survive? ⋮ Locating bifurcations in quasiperiodically forced systems ⋮ Bifurcation structure in a bimodal piecewise linear business cycle model ⋮ Dual star products and metric universality in symbolic dynamics of three letters. ⋮ Bifurcations in ecosystem models and their biological interpretation ⋮ Symmetry breaking and symmetry locking in equivariant circle maps ⋮ A Unified Renormalization Scheme for Two-Piecewise Monotonous Maps of the Interval ⋮ CATASTROPHE THEORETIC CLASSIFICATION OF NONLINEAR OSCILLATORS ⋮ Multiple attractors and boundary crises in a tri-trophic food chain ⋮ Order isomorphism under higher power shift and generic form of renormalization group equations in multimodal maps ⋮ Bifurcation structures in two-dimensional maps: the endoskeletons of shrimps ⋮ Two-parameter analysis of the scaling behavior at the onset of chaos: tricritical and pseudo-tricritical points ⋮ Chaos and the effect of noise in a model of three-wave mode coupling ⋮ Topological invariants and renormalization of Lorenz maps ⋮ A Genealogy for Finite Kneading Sequences of Bimodal Maps on the Interval ⋮ Symbolic dynamics of the sine-square map ⋮ Point Bifurcations and Bubbles for a Cubic Family ⋮ Bifurcations in ecosystem models and their biological interpretation ⋮ Symbolic dynamics and skeletons of circle maps ⋮ Cyclic star products and universalities in symbolic dynamics of trimodal maps ⋮ Food chain dynamics in the chemostat ⋮ Composite families of maps ⋮ Mixed-mode oscillation genealogy in a compartmental model of bone mineral metabolism ⋮ Symbolic dynamics of the Lorenz equations.
Cites Work
- A new type of period-doubling bifurcations in one-dimensional transformations with two extrema
- Global bifurcations of a periodically forced nonlinear oscillator
- Symbolic dynamics of the cubic map
- Universality and self-similarity in the bifurcations of circle maps
- Asymptotic chaos
- Transition to topological chaos for circle maps
- Structure of mappings of an interval with zero entropy
- On finite limit sets for transformations on the unit interval
- Boundary of Topological Chaos for Bimodal Maps of the Interval
- Hypergraphic Functions and Bifurcations in Recurrence Relations
- Stable Orbits and Bifurcation of Maps of the Interval
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item