Unfolding of resonant saddles and the Dulac time

DOI10.3934/dcds.2008.21.1221zbMath1153.37388OpenAlexW2313199121MaRDI QIDQ939284

Jordi Villadelprat, Pavao Mardešić, David Marin Perez

Publication date: 22 August 2008

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2008.21.1221

zbMATH Keywords

conjugacynormal formperiod functionbifurcation of critical periodsdulac time

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (13)

Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centres ⋮ Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: general setting ⋮ Extending to the complex line Dulac’s corner maps of non-degenerate planar singularities ⋮ Unfoldings of saddle-nodes and their Dulac time ⋮ On the upper bound of the criticality of potential systems at the outer boundary using the Roussarie-Ecalle compensator ⋮ On volume preserving almost Anosov flows ⋮ The criticality of centers of potential systems at the outer boundary ⋮ Analytic tools to bound the criticality at the outer boundary of the period annulus ⋮ Local analytic reduction of families of diffeomorphisms ⋮ On the period function in a class of generalized Lotka-Volterra systems ⋮ Bifurcations of zeros in translated families of functions and applications ⋮ Dulac time of a resonant saddle in the loud family ⋮ Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: local setting

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