Add to ORKGIn this paper we estimate fractal dimensions of almost periodic trajectories for a nonlinear evolution equation: ＄du/dt+A(t)u￥ni f(t)＄ . In the 2-frequency quasiperiodic case where ＄A(t+￥alpha)=A(t),＄ ＄￥alpha＄ is irrational, and ＄f(t+1)=＄ ＄f(t)＄ , by using Diophantine approximation, we can show that the dimension of the trajectory is majorized by ＄1/￥delta_{1}+1/￥delta_{2}＄ where ＄￥delta_{1},＄ ＄￥delta_{2}＄ are exponents of Holder continuity on ＄A(t),＄ ＄f(t)＄ , respectively. In the n-frequency case we can also estimate the dimension by using simultaneous Diophantine approximation
International audienceIn this chapter, we study some aspects of the chaotic behaviour of the time ev...
ABSTRACT. The limit set of the Kleinian group of a given doubly periodic Riccati equation is proved ...
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AbstractIn this paper we estimate fractal dimensions of almost periodic trajectories for a semilinea...
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In our previous papers ([4], [5], [6]) we have estimated dimensions for quasi peri-odic orbits by us...
International audienceWe consider particle motion in nonautonomous 1 degree of freedom Hamiltonian s...
On fractals and inhomogeneous structures that have been studied up to now, a single parameter, the s...
AbstractIn this paper, we estimate fractal dimensions of quasi-periodic orbits. Recently, Naito cons...
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Lyapunov exponents and fractal dimension of the twenty two chaotic oscillators avaluated by “Wolf’s ...
This paper treats a) the s.c. 'capacity" and 'alternate' fractal dirnension (fr.dim.], b) together w...
We study a quasi-linear evolution equation with nonlinear dynami- cal boundary conditions in a two ...
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In this work we look for conditions on the spectrum of the monodromy operator $P(t) $ determined fro...
International audienceIn this chapter, we study some aspects of the chaotic behaviour of the time ev...
ABSTRACT. The limit set of the Kleinian group of a given doubly periodic Riccati equation is proved ...
Here we study a class of second-order nonautonomous differential equations, and the corresponding pl...
AbstractIn this paper we estimate fractal dimensions of almost periodic trajectories for a semilinea...
We develop a method for studying fractal dimensions of forced almost periodic oscillations in variou...
In our previous papers ([4], [5], [6]) we have estimated dimensions for quasi peri-odic orbits by us...
International audienceWe consider particle motion in nonautonomous 1 degree of freedom Hamiltonian s...
On fractals and inhomogeneous structures that have been studied up to now, a single parameter, the s...
AbstractIn this paper, we estimate fractal dimensions of quasi-periodic orbits. Recently, Naito cons...
This study utilised fractal disk dimension characterization to investigate the time evolution of the...
Lyapunov exponents and fractal dimension of the twenty two chaotic oscillators avaluated by “Wolf’s ...
This paper treats a) the s.c. 'capacity" and 'alternate' fractal dirnension (fr.dim.], b) together w...
We study a quasi-linear evolution equation with nonlinear dynami- cal boundary conditions in a two ...
We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk...
In this work we look for conditions on the spectrum of the monodromy operator $P(t) $ determined fro...
International audienceIn this chapter, we study some aspects of the chaotic behaviour of the time ev...
ABSTRACT. The limit set of the Kleinian group of a given doubly periodic Riccati equation is proved ...
Here we study a class of second-order nonautonomous differential equations, and the corresponding pl...