Resynchronizing Dynamical Systems (2007)
Charles Tresser, Patrick A. Worfolk, Typeset Using Revt
Resynchronizing dynamical systems are important for certain chaotic signal masking methods. We demonstrate the dependence of the resynchronizing property of linear dynamical systems on choices of...
When An Infinitely-Renormalizable Endomorphism Of The Interval Can Be Smoothed (2007)
Charles Tresser, Amie Wilkinson
Let K be a closed subset of a smooth manifold M , and let f : K ! K be a continuous selfmap of K. We say that f is smoothable if it is conjugate to the restriction of a smooth map by a homeomorphism...
A Bell Theorem with no locality assumption (2006)
We prove here a version of Bell Theorem that does not assume locality. As a consequence classical realism, and not locality, is the common source of the violation by nature of all Bell Inequalities.
How much information can one store in a non-equilibrium medium? (2005)
Coullet, Pierre, Toniolo, Chiara, Tresser, Charles
It has recently been emphasized again that the very existence of stationary stable localized structures with short range interactions might allow to store information in non-equilibrium media,...
Any is not all: EPR and the Einstein-Tolman-Podolsky paper (2005)
In Bohm's version of the EPR gedanken experiment, the spin of the second particle along any vector is minus the spin of the other particle along the same vector. It seems that either the choice of...
Weak realism, counterfactuals, and decay of geometry at small scales (2005)
Two typical entanglements will be shown to stand on opposite sides on the issue of \emph{instrumental realism}, the issue of whether (as for EPR in the original form or EPRB, Bohm's versions using...
The simplest Bell's theorem, with or without locality (2005)
We prove here a version of Bell's Theorem that is simpler than any previous one. The contradiction of Bell's inequality with Quantum Mechanics in the new version is not cured by non-locality so that...
How much information can one store in a non-equilibrium medium? (2005)
Coullet, Pierre, Toniolo, Chiara, Tresser, Charles
It has recently been emphasized again that the very existence of stationary stable localized structures with short range interactions might allow to store information in non-equilibrium media,...
How much information can one store in a non-equilibrium medium? (2005)
Coullet, Pierre, Toniolo, Chiara, Tresser, Charles
It has recently been emphasized again that the very existence of stationary stable localized structures with short range interactions might allow to store information in non-equilibrium media,...
Introduction: Pattern formation at the turn of the millennium (2004)
Coullet, Pierre, Tresser, Charles
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A New Approach to Data Storage Using Localized Structures (2004)
Coullet, Pierre, Riera, Christophe, Tresser, Charles
In this paper we describe how to use the bifurcation structure of static localized solutions in one dimension to store information on a medium in such a way that no extrinsic grid is needed to locate...
On Entropy and Monotonicity for Real Cubic Maps (1998)
Milnor, John, Tresser, Charles
It has been known for some time that the topological entropy is a nondecreasing function of the parameter in the real quadratic family, which corresponds to the intuitive idea that more nonlinearity...
Stably non-synchronizable maps of the plane (1997)
Calvez, Patrice Le, Martens, Marco, Tresser, Charles, Worfolk, Patrick A.
Pecora and Carroll presented a notion of synchronization where an (n-1)-dimensional nonautonomous system is constructed from a given $n$-dimensional dynamical system by imposing the evolution of one...
Topological Conjugacy of Linear Endomorphisms of the 2-Torus (1997)
Roy Adler, Charles Tresser, Patrick A. Worfolk
. We describe two complete sets of numerical invariants of topological conjugacy for linear endomorphisms of the two-dimensional torus, i.e., continuous maps from the torus to itself which are...
Master-slave synchronization and the Lorenz equations (1997)
Neil Balmforth, Charles Tresser, Patrick Worfolk, Chai Wah Wu
Since the seminal remark by Pecora and Carroll that one can synchronize chaotic systems, the main example in the related literature has been the Lorenz equations. Yet this literature contains a...
Stably Non-Synchronizable Maps Of The Plane (1997)
Patrice Le Calvez, Marco Martens, Charles Tresser, PATRICK A. WORFOLK
. Pecora and Carroll presented a notion of synchronization where an (n \Gamma 1)-dimensional nonautonomous system is constructed from a given n-dimensional dynamical system by imposing the evolution...
Organization of parameter space for simple circle maps: the Farey web (1996)
Brucks, Karen M., Ringland, John, Tresser, Charles
We define the Farey web --- a collection of loci in the parameter plane of families of simple non-invertible maps of the circle. We prove some results about the arrangement of these loci and their...
Period doubling, entropy, and renormalization (1995)
We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point, i.e., the combinatorial description of the boundary of...
Piecewise Linear Models for the Quasiperiodic Transition to Chaos (1995)
Campbell, David K., Galeeva, Roza, Tresser, Charles, Uherka, David J.
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable...
Piecewise Linear Models for the Quasiperiodic Transition to Chaos (1995)
Campbell, David K, Galeeva, Roza, Tresser, Charles, Uherka, David J
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable...
Master-Slave Synchronization From the Point of View of Global Dynamics (1995)
Charles Tresser, Patrick A. Worfolk
We present a mathematical framework for the theory of a synchronization phenomenon for dynamical systems discovered by Pecora & Carroll. From this perspective, we can synchronize, using a single...
Forcing of periodic orbits for interval maps and renormalization of piecewise affine maps (1994)
Martens, Marco, Tresser, Charles
We prove that for continuous maps on the interval, the existence of an n-cycle, implies the existence of n-1 points which interwind the original ones and are permuted by the map. We then use this...
Epstein, Adam, Keen, Linda, Tresser, Charles
Consider the two-parameter family of real analytic maps $F_{a,b}:x \mapsto x+ a+{b\over 2\pi} \sin(2\pi x)$ which are lifts of degree one endomorphisms of the circle. The purpose of this paper is to...
Inducing, slopes, and conjugacy classes (1994)
Galeeva, Roza, Martens, Marco, Tresser, Charles
We show that the conjugacy class of an eventually expanding continuous piecewise affine interval map is contained in a smooth codimension 1 submanifold of parameter space. In particular conjugacy...
A monotonicity conjecture for real cubic maps (1993)
Dawson, Silvina P., Galeeva, Roza, Milnor, John W., Tresser, Charles
This is an outline of work in progress. We study the conjecture that the topological entropy of a real cubic map depends ``monotonely'' on its parameters, in the sense that each locus of constant...
A Genealogy for Finite Kneading Sequences of Bimodal Maps on the Interval (1993)
Ringland, John, Tresser, Charles
We generate all the finite kneading sequences of one of the two kinds of bimodal map on the interval, building each sequence uniquely from a pair of shorter ones. There is a single pair at generation...