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— Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex systems, there exist elements which can influence the dynamics of the system which are not well modelled or even known. One… (More)

- Fayçal Ben Adda, Jacky Cresson
- Applied Mathematics and Computation
- 2005

— This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the fractional embedding of differential operators and ordinary differential equations. We construct an operator combining in a symmetric way the left and right… (More)

We extend the DuBois-Reymond necessary optimality condition and Noether’s symmetry theorem to the scale relativity theory setting. Both Lagrangian and Hamiltonian versions of Noether’s theorem are proved, covering problems of the calculus of variations with functionals defined on sets of non-differentiable functions, as well as more general… (More)

- Jacky Cresson
- 2002

We discuss a rigorous foundation of the pure scale relativity theory for a one-dimensional space variable. We define several notions as ‘‘representation’’ of a continuous function, scale law and minimal resolution. We define precisely the meaning of a scale reference system and space reference system for non-differentiable one-dimensional manifolds. 2002… (More)

- Jacky Cresson
- 2008

This paper is twofold. In a first part, we extend the classical differential calculus to continuous non differentiable functions by developping the notion of scale calculus. The scale calculus is based on a new approach of continuous non differentiable functions by constructing a one parameter family of differentiable functions f(t, ǫ) such that f(t, ǫ) →… (More)

- Jacky Cresson
- Journal of dental research
- 1949

— Many problems of physics or biology involve very irregular objects like the rugged surface of a malignant cell nucleus or the structure of space-time at the atomic scale. We define and study non-differentiable deformations of the classical Cartesian space R which can be viewed as the basic bricks to construct irregular objets. They are obtain by taking… (More)

Let N be a smooth manifold and f : N → N be a C, l ≥ 2 diffeomorphism. Let M be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue of the λ-lemma in this case.

- Löıc Bourdin, Jacky Cresson, Isabelle Greff, Isabelle Greff
- 2017

— We prove a fractional Noether’s theorem for fractional Lagrangian systems invariant under a symmetry group both in the continuous and discrete cases. This provides an explicit conservation law (first integral) given by a closed formula which can be algorithmically implemented. In the discrete case, the conservation law is moreover computable in a finite… (More)