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184,441
Universal scaling of rotation intervals for quasiperiodically forced circle maps
"... We introduce a simplifying assumption which makes it possible to approximate the rotation number of an invertible quasiperiodically forced circle map by an integral in the limit of large forcing. We use this to describe universal scaling laws for the width of the nontrivial rotation interval of n ..."
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We introduce a simplifying assumption which makes it possible to approximate the rotation number of an invertible quasiperiodically forced circle map by an integral in the limit of large forcing. We use this to describe universal scaling laws for the width of the nontrivial rotation interval
The structure of modelocked regions in quasiperiodically forced circle maps
, 1999
"... Using a mixture of analytic and numerical techniques we show that the modelocked regions of quasiperiodically forced Arnold circle maps form complicated sets in parameter space. These sets are characterized by ‘pinchedoff ’ regions, where the width of the modelocked region becomes very small. By ..."
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Using a mixture of analytic and numerical techniques we show that the modelocked regions of quasiperiodically forced Arnold circle maps form complicated sets in parameter space. These sets are characterized by ‘pinchedoff ’ regions, where the width of the modelocked region becomes very small
ROTATION NUMBERS FOR QUASIPERIODICALLY FORCED MONOTONE CIRCLE MAPS
, 2000
"... Rotation numbers have played a central role in the study of (unforced) monotone circle maps. In such a case it is possible to obtain a priori bounds of the form ρ 1 n ≤ 1 n(yny0) ≤ ρ + 1 n, where 1 n(y ny 0) is an estimate of the rotation number obtained from an orbit of length n with initial co ..."
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Cited by 12 (3 self)
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condition y 0, and ρ is the true rotation number. This allows rotation numbers to be computed reliably and efficiently. Although Herman has proved that quasiperiodically forced circle maps also possess a well defined rotation number, independent of initial condition, the analogous bound does not appear
NormalInternal Resonances in QuasiPeriodically Forced Oscillators: A Conservative Approach
, 2002
"... We perform a bifurcation analysis of normalinternal resonances in parametrised families of quasiperiodically forced Hamiltonian oscillators, for small forcing. The unforced system is a one degree of freedom oscillator, called the `backbone' system; forced, the system is a skewproduct flow wi ..."
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Cited by 22 (18 self)
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We perform a bifurcation analysis of normalinternal resonances in parametrised families of quasiperiodically forced Hamiltonian oscillators, for small forcing. The unforced system is a one degree of freedom oscillator, called the `backbone' system; forced, the system is a skewproduct flow
PERIOD DOUBLING AND REDUCIBILITY IN THE QUASIPERIODICALLY FORCED LOGISTIC MAP
"... (Communicated by Lluis Alseda) Abstract. We study the dynamics of the Forced Logistic Map in the cylinder. We compute a bifurcation diagram in terms of the dynamics of the attracting set. Different properties of the attracting set are considered, such as the Lyapunov exponent and, in the case of hav ..."
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Cited by 8 (8 self)
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(Communicated by Lluis Alseda) Abstract. We study the dynamics of the Forced Logistic Map in the cylinder. We compute a bifurcation diagram in terms of the dynamics of the attracting set. Different properties of the attracting set are considered, such as the Lyapunov exponent and, in the case
Globally and locally attractive solutions for quasiperiodically forced systems
 J. Math. Anal. Appl
"... We consider a class of differential equations, x ̈ + γx ̇ + g(x) = f(ωt), with ω ∈ Rd, describing onedimensional dissipative systems subject to a periodic or quasiperiodic (Diophantine) forcing. We study existence and properties of trajectories with the same quasiperiodicity as the forcing. For ..."
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Cited by 16 (10 self)
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We consider a class of differential equations, x ̈ + γx ̇ + g(x) = f(ωt), with ω ∈ Rd, describing onedimensional dissipative systems subject to a periodic or quasiperiodic (Diophantine) forcing. We study existence and properties of trajectories with the same quasiperiodicity as the forcing
RESPONSE SOLUTIONS FOR QUASIPERIODICALLY FORCED, DISSIPATIVE WAVE EQUATIONS
"... Abstract. We consider several models of nonlinear wave equations subject to very strong damping and quasiperiodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response solutions (i.e., quasiperiodic solutions with the ..."
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Abstract. We consider several models of nonlinear wave equations subject to very strong damping and quasiperiodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response solutions (i.e., quasiperiodic solutions
Superstable periodic orbits of 1d maps under quasiperiodic forcing and reducibility loss∗
, 2013
"... Let gα be a oneparameter family of onedimensional maps with a cascade of period doubling bifurcations. Between each of these bifurcations, a superstable periodic orbit is known to exist. An example of such a family is the wellknown logistic map. In this paper we deal with the effect of a quasipe ..."
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Cited by 1 (1 self)
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curves. If the map satifies an extra condition (condition satisfied by the quasiperiodically forced logistic map) then we show that, from each superattracting point of the unperturbed map, two reducibility loss bifurcation curves are born. This means that these curves are present for all the cascade. 1
Hill's Equation With QuasiPeriodic Forcing: Resonance Tongues, Instability Pockets and Global Phenomena
, 1998
"... A simple example is considered of Hill's equation x+ (a 2 +b p(t))x = 0; where the forcing term p; instead of periodic, is quasiperiodic with two frequencies. A geometric exploration is carried out of certain resonance tongues, containing instability pockets. This phenomenon in the perturb ..."
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Cited by 28 (8 self)
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A simple example is considered of Hill's equation x+ (a 2 +b p(t))x = 0; where the forcing term p; instead of periodic, is quasiperiodic with two frequencies. A geometric exploration is carried out of certain resonance tongues, containing instability pockets. This phenomenon
Results 1  10
of
184,441