Abstract
Horseshoe maps have played an important role in the study of nonlinear dynamical systems. Here we study maps associated to two simple physical systems: a four-hill potential and an open billiard. They turn out to be very different from the standard horseshoe maps: one iteration stretches and folds a square in phase space an infinite number of times before placing it across itself. In this paper we explore in further depth these infinite horseshoe maps. We show that the infinite folding action requires that the maps are not defined in part of the rectangle. Our exploration also shows that infinite horseshoes provide valuable information on the complexity of the system. In particular, they provide a visual way to code the wide variety of complex orbits existing in the dynamical systems considered.
| Original language | English |
|---|---|
| Pages (from-to) | 866-871 |
| Number of pages | 6 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 22 |
| Issue number | 1-3 |
| DOIs | |
| Publication status | Published - May 1 2015 |
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Keywords
- Chaotic scattering
- Horseshoes
- Open billiard
ASJC Scopus subject areas
- Modelling and Simulation
- Numerical Analysis
- Applied Mathematics
Cite this
Infinite horseshoes and complex dynamics in physical systems. / Zambrano, Samuel; Sanjuán, Miguel A F.
In: Communications in Nonlinear Science and Numerical Simulation, Vol. 22, No. 1-3, 01.05.2015, p. 866-871.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Infinite horseshoes and complex dynamics in physical systems
AU - Zambrano, Samuel
AU - Sanjuán, Miguel A F
PY - 2015/5/1
Y1 - 2015/5/1
N2 - Horseshoe maps have played an important role in the study of nonlinear dynamical systems. Here we study maps associated to two simple physical systems: a four-hill potential and an open billiard. They turn out to be very different from the standard horseshoe maps: one iteration stretches and folds a square in phase space an infinite number of times before placing it across itself. In this paper we explore in further depth these infinite horseshoe maps. We show that the infinite folding action requires that the maps are not defined in part of the rectangle. Our exploration also shows that infinite horseshoes provide valuable information on the complexity of the system. In particular, they provide a visual way to code the wide variety of complex orbits existing in the dynamical systems considered.
AB - Horseshoe maps have played an important role in the study of nonlinear dynamical systems. Here we study maps associated to two simple physical systems: a four-hill potential and an open billiard. They turn out to be very different from the standard horseshoe maps: one iteration stretches and folds a square in phase space an infinite number of times before placing it across itself. In this paper we explore in further depth these infinite horseshoe maps. We show that the infinite folding action requires that the maps are not defined in part of the rectangle. Our exploration also shows that infinite horseshoes provide valuable information on the complexity of the system. In particular, they provide a visual way to code the wide variety of complex orbits existing in the dynamical systems considered.
KW - Chaotic scattering
KW - Horseshoes
KW - Open billiard
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U2 - 10.1016/j.cnsns.2014.07.013
DO - 10.1016/j.cnsns.2014.07.013
M3 - Article
AN - SCOPUS:84916890116
VL - 22
SP - 866
EP - 871
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
IS - 1-3
ER -