Symbolic sequences of one-dimensional quadratic maps points

1998 ◽  
Vol 256 (3-4) ◽  
pp. 369-382 ◽  
Author(s):  
G. Pastor ◽  
M. Romera ◽  
J.C. Sanz-Martı́n ◽  
F. Montoya
Keyword(s):  
One Dimensional ◽  
Quadratic Maps ◽  
Symbolic Sequences

An approach to the ordering of one-dimensional quadratic maps

1996 ◽  
Vol 7 (4) ◽  
pp. 565-584 ◽  
Author(s):  
G. Pastor ◽  
M. Romera ◽  
F. Montoya
Keyword(s):  
One Dimensional ◽  
Quadratic Maps

How to work with one-dimensional quadratic maps

2003 ◽  
Vol 18 (5) ◽  
pp. 899-915 ◽  
Author(s):  
G. Pastor ◽  
M. Romera ◽  
G. Álvarez ◽  
F. Montoya
Keyword(s):  
One Dimensional ◽  
Quadratic Maps

THE DISTRIBUTION OF PERIODIC AND APERIODIC PATTERN EVOLUTIONS IN RINGS OF DIFFUSIVELY COUPLED MAPS

2001 ◽  
Vol 11 (10) ◽  
pp. 2647-2661 ◽  
Author(s):  
PEDRO G. LIND ◽  
JOÃO A. M. CORTE-REAL ◽  
JASON A. C. GALLAS
Keyword(s):  
Boundary Conditions ◽  
Parameter Space ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
One Dimensional ◽  
Quadratic Maps ◽  
Coupled Maps

This paper reports histograms showing the detailed distribution of periodic and aperiodic motions in parameter-space of one-dimensional lattices of diffusively coupled quadratic maps subjected to periodic boundary conditions. Particular emphasis is given to the parameter domains where lattices support traveling patterns.

scholarly journals Invariant measures for some one-dimensional attractors

1982 ◽  
Vol 2 (3-4) ◽  
pp. 317-337 ◽  
Author(s):  
M. V. Jacobson
Keyword(s):  
Invariant Measures ◽  
Small Perturbations ◽  
One Dimensional ◽  
Quadratic Maps ◽  
Hyperbolic Attractors

AbstractWe consider certain non-invertible maps of the square which are extensions of the quadratic maps of the interval and their small perturbations. We show that several maps of the type possess attractors which are not hyperbolic but have invariant measures similar to Bowen-Ruelle measures for hyperbolic attractors.

Misiurewicz point patterns generation in one-dimensional quadratic maps

2001 ◽  
Vol 292 (1-4) ◽  
pp. 207-230 ◽  
Author(s):  
G. Pastor ◽  
M. Romera ◽  
G. Alvarez ◽  
F. Montoya
Keyword(s):  
One Dimensional ◽  
Quadratic Maps ◽  
Point Patterns

Misiurewicz points in one-dimensional quadratic maps

1996 ◽  
Vol 232 (1-2) ◽  
pp. 517-535 ◽  
Author(s):  
M. Romera ◽  
G. Pastor ◽  
F. Montoya
Keyword(s):  
One Dimensional ◽  
Quadratic Maps

EXTENDING CHUA'S GLOBAL EQUIVALENCE THEOREM ON WOLFRAM'S NEW KIND OF SCIENCE

2007 ◽  
Vol 17 (12) ◽  
pp. 4245-4259 ◽  
Author(s):  
JUNBIAO GUAN ◽  
SHAOWEI SHEN ◽  
CHANGBING TANG ◽  
FANGYUE CHEN
Keyword(s):  
Cellular Automata ◽  
Equivalence Class ◽  
Symbolic Dynamics ◽  
Equivalence Theorem ◽  
Equivalence Classes ◽  
Local Rule ◽  
One Dimensional ◽  
Symbolic Space ◽  
Symbolic Sequences

We establish the relation between the extended (i.e. I = ∞) one-dimensional binary Cellular Automata (1D CA) and the bi-infinite symbolic sequences in symbolic dynamics. That is, the 256 local rules of 1D CA correspond to 256 local rule mappings in the symbolic space. By employing the two homeomorphisms T† and [Formula: see text] from [Chua et al., 2004] for finite I, we classify these 256 local rule mappings into the same 88 equivalence classes identified in [Chua et al., 2004] and [Chua, 2006]. Different mappings in the same equivalence class are mutually topologically conjugate.

Codimension-2 Border Collision, Bifurcations in One-Dimensional, Discontinuous Piecewise Smooth Maps

2014 ◽  
Vol 24 (02) ◽  
pp. 1450024 ◽  
Author(s):  
Laura Gardini ◽  
Viktor Avrutin ◽  
Irina Sushko
Keyword(s):  
Discontinuity Point ◽  
Piecewise Smooth ◽  
One Dimensional ◽  
Smooth Maps ◽  
Border Collision Bifurcations ◽  
Piecewise Smooth Maps ◽  
Symbolic Sequences ◽  
Bifurcation Structures ◽  
Local Monotonicity ◽  
Parameter Values

We consider a two-parametric family of one-dimensional piecewise smooth maps with one discontinuity point. The bifurcation structures in a parameter plane of the map are investigated, related to codimension-2 bifurcation points defined by the intersections of two border collision bifurcation curves. We describe the case of the collision of two stable cycles of any period and any symbolic sequences. For this case, we prove that the local monotonicity of the functions constituting the first return map defined in a neighborhood of the border point at the parameter values related to the codimension-2 bifurcation point determines, under suitable conditions, the kind of bifurcation structure originating from this point; this can be either a period adding structure, or a period incrementing structure, or simply associated with the coupling of colliding cycles.

Harmonic structure of one-dimensional quadratic maps

1997 ◽  
Vol 56 (2) ◽  
pp. 1476-1483 ◽  
Author(s):  
G. Pastor ◽  
M. Romera ◽  
F. Montoya
Keyword(s):  
Harmonic Structure ◽  
One Dimensional ◽  
Quadratic Maps
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