Some lemmas about dynamical systems.
Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point
Some numerical studies of dynamical systems
Some perturbation results for non-linear problems
We discuss the existence of closed geodesic on a Riemannian manifold and the existence of periodic solution of second order Hamiltonian systems.
Some pinching deformations of the Fatou function
We are interested in deformations of Baker domains by a pinching process in curves. In this paper we deform the Fatou function , depending on the curves selected, to any map of the form , p/q a rational number. This process deforms a function with a doubly parabolic Baker domain into a function with an infinite number of doubly parabolic periodic Baker domains if p = 0, otherwise to a function with wandering domains. Finally, we show that certain attracting domains can be deformed by a pinching...
Some unresolved issued in non-linear population dynamics.
The Lyapunov exponent is a statistic that measures the sensitive dependence of the dynamic behaviour of a system on its initial conditions. Estimates of Lyapunov exponents are often used to characterize the qualitative population dynamics of insect time series. The methodology for estimation of the exponent for an observed, noisy, short ecological time series is still under development. Some progress has been made recently in providing measures of error for these exponents. Studies that do not account...
Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators.
Special directions on contact metric manifolds of negative -sectional curvature
Spectral properties of G-symbolic Morse shifts
Spectral theta series of operators with periodic bicharacteristic flow
The theta series is a classical example of a modular form. In this article we argue that the trace , where is a self-adjoint elliptic pseudo-differential operator of order 1 with periodic bicharacteristic flow, may be viewed as a natural generalization. In particular, we establish approximate functional relations under the action of the modular group. This allows a detailed analysis of the asymptotics of near the real axis, and the proof of logarithm laws and limit theorems for its value...
SRB measures for non-hyperbolic systems with multidimensional expansion
Stability and genericity in dynamical systems
Stability of Orbit spaces of Endomorphisms.
Stability of the densities of invariant measures for piecewise affine expanding non-renormalizable maps
Stabilizing the chaotic dynamics of the Lü system.
Stable and non-stable non-chaotic maps of the interval
Stable ergodicity and julienne quasi-conformality
In this paper we dramatically expand the domain of known stably ergodic, partially hyperbolic dynamical systems. For example, all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property are stably ergodic. Our main tools are the new concepts – julienne density point and julienne quasi-conformality of the stable and unstable holonomy maps. Julienne quasi-conformal holonomy maps preserve all julienne density points.
Stable ergodicity of skew products
Stable intersections of Cantor sets and homoclinic bifurcations
Staircase baker's map generates flaring-type time series.