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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 classes have empty interior. This is based... more
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 classes have empty interior. This is based on a study of the relation between induced Markov maps and ergodic theoretical behavior.
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It is well known that different preparations of a mixed state cannot be distinguished by a measurement of that state. Yet we show that some other experiments let us make this distinction despite a very general belief that this would not... more
It is well known that different preparations of a mixed state cannot be distinguished by a measurement of that state. Yet we show that some other experiments let us make this distinction despite a very general belief that this would not be possible. Issues in quantum cryptography that prompted this work are only briefly mentioned in this letter.
Research Interests: Mathematics and Physics
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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 this version allows one to single out... more
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 this version allows one to single out classical realism, and not locality, as the common source of all false inequalities of Bell's type.
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... Transition to topological chaos for circle maps. RS Mackay. ... RS MacKay and C. Tresser Transition to topological chaos for circle maps 0 I '41r In O h MRN 9C N lR o 207 Ve CUN o CX n Z7 .z IO 3 E an c 0 c n5 c .vooc, 3... more
... Transition to topological chaos for circle maps. RS Mackay. ... RS MacKay and C. Tresser Transition to topological chaos for circle maps 0 I '41r In O h MRN 9C N lR o 207 Ve CUN o CX n Z7 .z IO 3 E an c 0 c n5 c .vooc, 3 .oco .'u 3 3 oo OU v 1 5 G . C 7 c UOU v C oc O . d Ll. ...
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Mixing a symbolic approach to the dynamics of the period-doubling operators, recent results by Sullivan on the renormalization for real analytic maps, and some confidence, a global picture emerges for the structure of the boundary of... more
Mixing a symbolic approach to the dynamics of the period-doubling operators, recent results by Sullivan on the renormalization for real analytic maps, and some confidence, a global picture emerges for the structure of the boundary of positive topological entropy in spaces of smooth endomorphisms of the interval. Previous address: Department of Theoretical Physics (CNRS), Parc Valrose, 06034 Nice Cedex, France.
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Given a homeomorphism f of the circle, any splitting of this circle in two semiopen arcs induces a coding process for the orbits of f, which can be determined by recording the successive arcs visited by the orbit. The problem of... more
Given a homeomorphism f of the circle, any splitting of this circle in two semiopen arcs induces a coding process for the orbits of f, which can be determined by recording the successive arcs visited by the orbit. The problem of describing these codes has a two hundred year history (that we briefly recall) in the particular case when the arcs are limited by a point and its image; in modern language, it is the kneading theory of such maps, and as such is relevant for our understanding of dynamical problems involving oscillations. This paper deals with questions attached to the general case, a problem considered by many mathematicians in the 50’s and 60’s in the case where f is a rotation, and which has recently found some applications in physiology. We show that, except for trivial cases, any code determines the rotation number, up to the orientation, of the homeomorphism which generates it. In the case the code is periodic, we can also determine whether or not it can be generated in this way. An equivalent problem in arithmetic consists of finding ±p, knowing a collection of classes in Z/qZ of the form {m,m+p,...,m+(k−1)p}, where 2≤k≤q−2 and p and q are relatively prime. We describe this equivalence, and give simple solutions of the decoding problem both in the dynamical context and in the number theoretic context.
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We propose a rough classification for volume contracting flows in R3 with chaotic behavior. In the simplest cases, one looks at the nature of a homoclinic loop for the flow. Most configurations have been studied at length in the... more
We propose a rough classification for volume contracting flows in R3 with chaotic behavior. In the simplest cases, one looks at the nature of a homoclinic loop for the flow. Most configurations have been studied at length in the literature; here we examine briefly the ``forgotten" case
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Mappings of the plane, introduced by M. Hnon and R. Lozi, are presented as perturbations of endomorphisms of the line. When some heteroclinic tangencies occur, which allow topological conjugacy between the corresponding endomorphisms, and... more
Mappings of the plane, introduced by M. Hnon and R. Lozi, are presented as perturbations of endomorphisms of the line. When some heteroclinic tangencies occur, which allow topological conjugacy between the corresponding endomorphisms, and arbitrarily close to the endomorphisms case, we prove the nonexistence of topological conjugacy between Hnon mapping and Lozi mapping. The proof, as well as related results,
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ABSTRACT Toward the middle of 2001, the authors started arguing that fractals are important when discussing the operational resilience of information systems and related computer sciences issues such as artificial intelligence. But in... more
ABSTRACT Toward the middle of 2001, the authors started arguing that fractals are important when discussing the operational resilience of information systems and related computer sciences issues such as artificial intelligence. But in order to argue along these lines it turned out to be indispensable to define fractals so as to let one recognize as fractals some sets that are very far from being self similar in the (usual) metric sense. This paper is devoted to define (in a loose sense at least) fractals in ways that allow for instance all the Cantor sets to be fractals and that permit to recognize fractality (the property of being fractal) in the context of the information technology issues that we had tried to comprehend. Starting from the meta-definition of a fractal as an “object with non-trivial structure at all scales” that we had used for long, we ended up taking these words seriously. Accordingly we define fractals in manners that depend both on the structures that the fractals are endowed with and the chosen sets of structure compatible maps, i.e., we approach fractals in a category-dependent manner. We expect that this new approach to fractals will contribute to the understanding of more of the fractals that appear in exact and other sciences than what can be handled presently.
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Research Interests: Mathematics, Applied Mathematics, Computer Science, Physics, Nonlinear dynamics, and 11 moreStatistical Physics, Medicine, Entropy, Software, Chaos, Non-equilibrium thermodynamics, Mathematical Computing, Information Storage and Retrieval, Molecular Computers, Numerical Analysis and Computational Mathematics, and Computing Methodologies
... Some flesh on the skeleton: The bifurcation structure of bimodal maps. Source, Physica D archive Volume 27 , Issue 3 (August 1987) table ...
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... help Tackle the Majority of Managerial Problems? 36 Supply Chain Forum An International Journal Vol. 4 - N°1 - 2003 www.supplychain-forum.com Charles Tresser Mathematical Sciences Department IBM Thomas J. Watson Research Center, USA... more
... help Tackle the Majority of Managerial Problems? 36 Supply Chain Forum An International Journal Vol. 4 - N°1 - 2003 www.supplychain-forum.com Charles Tresser Mathematical Sciences Department IBM Thomas J. Watson Research Center, USA tresser@us.ibm.com ...
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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 the information. We demonstrate that... more
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 the information. We demonstrate that these principles, deduced from the mathematics adapted to describe one-dimensional media, also allow one to store information on two-dimensional media.
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We describe an embedding of the Farey web, an extension of the better-known Farey tree, in the parameter space of simple families of circle maps. We also discuss some consequences of this embedding on the organization of frequency-locking... more
We describe an embedding of the Farey web, an extension of the better-known Farey tree, in the parameter space of simple families of circle maps. We also discuss some consequences of this embedding on the organization of frequency-locking and on topological properties of the boundary between simple and complicated dynamics.
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