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    • Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs Validation and Extraction of Global Nature
    Tác giả : Jean-Philippe, Lessard; Kaname, Matsue; Akitoshi, Takayasu;  Người hướng dẫn: -;  Đồng tác giả: - (2023)

    In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining dynamical systems machinery (e.g., compactifications, timescale desingularizations of vector fields) with tools from computer-assisted proofs (e.g., rigorous integrators, the parameterization method for invariant manifolds), these blow-up solutions are obtained as trajectories on local stable manifolds of hyperbolic saddle equilibria at infinity. With the help of computer-assisted proofs, global trajectories on stable manifolds, inducing blow-up solutions, provide a global picture organized by global-in-time solutions and blow-up solutions simultaneously.