Topological Entropy in a Parameter Range of the Standard Map(General and Mathematical Physics)
スポンサーリンク
概要
- 論文の詳細を見る
We combine the trellis method and the braid method, and by estimating the lower bounds of the topological entropy of the standard map for a certain parameter range, we follow the change of the topological entropy. The trellis in a tangency situation of the stable and unstable manifolds is constructed. Applying the trellis method to this trellis, the lower bound of topological entropy is calculated. There exist systems in which the trellis method can not be applicable. For such systems, we look for non-Birkhoff periodic orbits existent in the trellises, form braids from those periodic orbits, and estimate the topological entropy from their braid types. We perform these tasks for a sequence of trellises and numerically visualize the change in the topological entropy. In addition, we take particular sequence of connecting orbits to obtain homoclinic or heteroclinic orbits. As a natural extension, we assign topological entropy to these homoclinic and heteroclinic orbits.
- 理論物理学刊行会の論文
- 2009-04-25
著者
-
TANIKAWA Kiyotaka
National Astronomical Observatory
-
Yamaguchi Yoshihiro
Teikyo Heisei Univ. Tokyo Jpn
-
Tanikawa Kiyotaka
National Astronomical Obseruatory
-
Yamaguchi Yoshihiro
Teikyo Heisei Univ. Chiba Jpn
関連論文
- A New Interpretation of the Symbolic Codes for the Henon Map(General and Mathematical Physics)
- Solar Eclipses in the First Half of the Chunqiu Period
- Dynamical Ordering of Periodic Accelerator Modes in the Standard Mapping(Condensed Matter and Statistical Physics)
- Generalized Dynamical Ordering and Topological Entropy in the Henon Map(Condensed Matter and Statistical Physics)
- A New Set of Variables in the Three-Body Problem
- Topological Entropy in a Forced Duffing System(Condensed Matter and Statistical Physics)
- Non-Birkhoff Periodic Orbits in a Circle Map
- Dynamical Ordering of Non-Birkhoff Orbits and Topological Entropy in the Standard Mapping
- Increase of Topological Entropy until the Three-Fold Horseshoe is Completed(Condensed Matter and Statistical Physics)
- A New Interpretation of the Symbolic Codes for the Henon Map. II(General and Mathematical Physics)
- Generalized Horseshoes in the Standard Mapping(Condensed Matter and Statistical Physics)
- Units of Time in Ancient China and Japan
- A Solar Eclipse Versified in the Shijing
- ΔT and the Tidal Acceleration of the Lunar Motion from Eclipses Observed at Plural Sites
- Dynamical Ordering of Symmetric Periodic Orbits for the Area Preserving Henon Map(Condensed Matter and Statistical Physics)
- Order of Appearance of Homoclinic Points for the Henon Map(Condensed Matter and Statistical Physics)
- Stability of Terrestrial Protoplanet Systems and Alignment of Orbital Elements
- Improvement of the Triple-Encounter Criterion
- Dynamical Ordering of Non-Birkhoff Periodic Orbits in a Forced Pendulum
- A Condition for the Existence of Homoclinic Intersection in C^2 Standard-Like Mappings
- Topological Entropy in a Forced Duffing System
- A Remark on the Smoothness of Critical KAM Curves in the Standard Mapping : Condensed Matter and Statistical Physics
- Running Homoclinic and Periodic Points in Standard-Like Mappings
- Non-Symmetric Periodic Points in Reversible Maps : Examples from the Standard Map(Condensed Matter and Statistical Physics)
- Symmetric Periodic Orbits and Topological Entropy in the Two-Dimensional Cubic Map(Condensed Matter and Statistical Physics)
- Periodic Orbits in the Quadruply Reversible Non-Twist Harper Map
- Symmetrical Non-Birkhoff Period-3 Orbits in Standard-Like Mappings
- Oscillatory Orbits in the Standard Mapping (Condensed Matter and Statistical Physics)
- Non-Symmetric Non-Birkhoff Period-2 Orbits in the Standard Mapping
- Non-Birkhoff Orbits with 2n Turning Points in the Standard Map
- Topological Entropy in a Parameter Range of the Standard Map(General and Mathematical Physics)
- On Mather's Connecting Orbits in Standard Mapping(Condensed Matter and Statistical Physics)
- Non-Birkhoff Periodic Orbits of Farey Type and Dynamical Ordering in the Standard Mapping. II(Condensed Matter and Statistical Physics)
- Birkhoff Periodic Orbits in the Standard-Like Maps
- On the Totality of the Eclipse in AD 628 in the Nihongi
- Forcing Relations for Homoclinic Orbits of the Reversible Horseshoe Map(General and Mathematical Physics)
- Subsystems in a Stable Planetary System
- Phase Transitions of Route Patterns in the Steiner's Problem with Four Cities
- On the Symmetric Collinear Four-Body Problem
- Non-Birkhoff Periodic Orbits of Farey Type and Dynamical Ordering in the Standard Mapping(Condensed Matter and Statistical Physics)
- Nonsymmetric Saddle-Node Pairs for the Reversible Smale Horseshoe Map(General and Mathematical Physics)
- Non-Birkhoff Orbits with 2n Turning Points in the Standard Map
- New Period-Doubling and Equiperiod Bifurcations of the Reversible Area-Preserving Map(General and Mathematical Physics)
- Nonsymmetric Saddle-Node Pairs for the Reversible Smale Horseshoe Map
- On the Error Reduction of a Simple Symplectic Integrator
- Generalized Horseshoes in the Standard Mapping(Condensed Matter and Statistical Physics)