Antonio Giorgilli

Antonio Giorgilli's AcademicInfluence.com Rankings

Antonio Giorgilli

Mathematics

#7678

World Rank

#10418

Historical Rank

Mathematical Physics

#60

World Rank

#71

Historical Rank

Measure Theory

#2703

World Rank

#3229

Historical Rank

mathematics Degrees

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Mathematics

Antonio Giorgilli's Degrees

PhD Physics University of Milan

Why Is Antonio Giorgilli Influential?

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According to Wikipedia, Antonio Giorgilli is an Italian mathematical physicist, known for his work on the perturbative theory of Hamiltonian systems with applications to studies of orbital stability for major and minor planets.

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Antonio Giorgilli's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory (1980) (1518)
Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application (1980) (807)
On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms (1994) (311)
Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem (1989) (216)
A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems (1985) (176)
Superexponential stability of KAM tori (1995) (159)
Formal integrals for an autonomous Hamiltonian system near an equilibrium point (1978) (119)
A proof of Kolmogorov’s theorem on invariant tori using canonical transformations defined by the Lie method (1984) (116)
Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II (1987) (107)
On the number of isolating integrals in Hamiltonian systems (1978) (98)
On the stability of the lagrangian points in the spatial restricted problem of three bodies (1991) (94)
Rigorous estimates for the series expansions of Hamiltonian perturbation theory (1985) (92)
Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems (1993) (83)
On the problem of energy equipartition for large systems of the Fermi-Pasta-Ulam type: analytical and numerical estimates (1992) (79)
Notes on exponential stability of Hamiltonian systems (2003) (75)
Exponentially long times to equipartition in the thermodynamic limit (2004) (73)
Localization of energy in FPU chains (2004) (69)
Invariant Tori in the Secular Motions of the Three-body Planetary Systems (2000) (66)
Rigorous results on the power expansions for the integrals of a Hamiltonian system near an elliptic equilibrium point (1988) (60)
Kolmogorov theorem and classical perturbation theory (1997) (58)
A computer program for integrals of motion (1984) (57)
A Nekhoroshev-type theorem for Hamiltonian systems with infinitely many degrees of freedom (1988) (56)
The Fermi—Pasta—Ulam Problem and the Metastability Perspective (2007) (55)
Kolmogorov and Nekhoroshev theory for the problem of three bodies (2009) (54)
Exponential stability for time dependent potentials (1992) (53)
On the reliability of numerical studies of stochasticity I: Existence of time averages (1978) (50)
The Fermi-Pasta-Ulam Problem (2002) (49)
INVARIANT TORI IN THE SUN{JUPITER{SATURN SYSTEM (2006) (46)
Exponential law for the equipartition times among translational and vibrational degrees of freedom (1987) (46)
An efficient procedure to compute fractal dimensions by box counting (1986) (44)
Boltzmann's ultraviolet cutoff and Nekhoroshev's theorem on Arnold diffusion (1984) (43)
On a connection between KAM and Nekhoroshev's theorems (1995) (42)
Nonconvergence of formal integrals: II. Improved estimates for the optimal order of truncation (2004) (41)
On the stability of the secular evolution of the planar Sun-Jupiter-Saturn-Uranus system (2010) (41)
On classical series expansions for quasi-periodic motions (1997) (41)
Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part I (1987) (41)
Invariant KAM tori and global stability for Hamiltonian systems (1997) (40)
Improved estimates on the existence of invariant tori for Hamiltonian systems (2000) (36)
The Fermi-Pasta-Ulam problem as a challenge for the foundations of physics. (2005) (32)
Methods of algebraic manipulation in perturbation theory (2013) (30)
Numerical investigations on a chain of weakly coupled rotators in the light of classical perturbation theory (1985) (30)
CONSTRUCTION OF KOLMOGOROV'S NORMAL FORM FOR A PLANETARY SYSTEM (2005) (29)
A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems (2010) (29)
Classical perturbation theory for systems of weakly coupled rotators (1985) (29)
Unstable equilibria of Hamiltonian systems (2001) (29)
Non-convergence of formal integrals of motion (2003) (29)
Quantitative methods in classical perturbation theory (1995) (28)
On the reliability of numerical studies of stochasticity (1979) (26)
Bifurcations and complex instability in a 4-dimensional symplectic mapping (1988) (26)
Fermi-Pasta-Ulam phenomenon for generic initial data. (2007) (26)
Apparent fractal dimensions in conservative dynamical systems (1986) (25)
A CLASSICAL SELF-CONTAINED PROOF OF KOLMOGOROV'S THEOREM ON INVARIANT TORI (1999) (25)
Packets of resonant modes in the Fermi–Pasta–Ulam system (2012) (24)
Further results on universal properties in conservative dynamical systems (1980) (24)
Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability in the light of Kolmogorov and Nekhoroshev theories (2017) (24)
Resonances and asymptotic behavior of Birkhoff series (1983) (23)
On the dynamics in the asteroids belt. Part II: Detailed study of the main resonances (1989) (23)
An Extensive Adiabatic Invariant for the Klein–Gordon Model in the Thermodynamic Limit (2013) (22)
CONVERGENCE RADIUS IN THE POINCARE-SIEGEL PROBLEM (2010) (21)
An extension of the Poincaré-Fermi theorem on the nonexistence of invariant manifolds in nearly integrable Hamiltonian systems (1982) (20)
Some remarks on the problem of ergodicity of the Standard Map (2000) (20)
Extensive Adiabatic Invariants for Nonlinear Chains (2012) (19)
On the dynamics in the asteroids belt. Part I : General theory (1989) (19)
Chaotic motions and transition to stochasticity in the classical problem of the heavy rigid body with a fixed point (1981) (18)
Local chaotic behaviour in the Fermi-Pasta-Ulam system (2005) (17)
Quantitative perturbation theory by successive elimination of harmonics (1993) (17)
Classical electrodynamics as a nonlinear dynamical system (1989) (17)
On the role of high order resonances in normal forms and in separatrix splitting (1997) (16)
Exponentially stable manifolds in the neighbourhood of elliptic equilibria (2006) (15)
On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems (2014) (13)
On the convergence of an algorithm constructing the normal form for lower dimensional elliptic tori in planetary systems (2014) (12)
FPU phenomenon for generic initial data (2007) (11)
On a theorem of Lyapounov (2012) (11)
Estimates for normal forms of differential equations near an equilibrium point (1988) (10)
On the numerical optimization of KAM estimates by classical perturbation theory (1988) (10)
A Series Expansion for the Time Autocorrelation of Dynamical Variables (2011) (9)
Normal Form and Energy Conservation of High Frequency Subsystems Without Nonresonance Conditions (2013) (8)
ON THE REPRESENTATION OF MAPS BY LIE TRANSFORMS (2012) (8)
On a weakened form of the averaging principle in multifrequency systems (1995) (8)
Visualization of a Hyperbolic Structure in Area Preserving Maps (1997) (8)
Small denominators and exponential stability: From Poincaré to the present time (1998) (7)
Classical constructive methods in KAM theory (1998) (7)
Stochasticity thresholds in a lattice field theory (1980) (6)
Numerical computations of Liapunov exponents for a discretized one-dimensional nonlinear Klein-Gordon equation (1983) (6)
Dynamical Systems and Thermodynamics (2006) (6)
Effective stability in Hamiltonian systems in the light of Nekhoroshev's theorem (1989) (6)
Improved convergence estimates for the Schröder–Siegel problem (2015) (6)
The Dynamical Foundations of Classical Statistical Mechanics and the Boltzmann-Jeans Conjecture (1994) (6)
Hamiltonian Dynamics. Theory and Applications (2005) (5)
Long Time Stability for the Main Problem of Artificial Satellites (1997) (5)
Characterization of vibrational transition modes by use of normal forms (1993) (5)
Representation of a 2-power as sum of k 2-powers: A recursive formula (2013) (5)
Canonical perturbation theory for nearly integrable systems (2006) (5)
Notes on Hamiltonian Dynamical Systems (2022) (4)
On the measure of the structure around an invariant KAM torus. (1996) (3)
High-order control for symplectic maps (2015) (3)
A KEPLER’S NOTE ON SECULAR INEQUALITIES (2014) (3)
Relevance of Exponentially Large Time Scales in Practical Applications: Effective Fractal Dimensions in Conservative Dynamical Systems (1988) (2)
Energy Equipartition and Nekhoroshev-Type Estimates for Large Systems (1995) (2)
On the persistence of ordered motions in Hamiltonian systemsand the problem of energy partition (1986) (2)
On the relativistic Lagrange-Laplace secular dynamics for extrasolar systems (2014) (2)
On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems (2014) (1)
An Extensive Adiabatic Invariant for the Klein–Gordon Model in the Thermodynamic Limit (2014) (1)
Hamiltonian dynamics theory and applications : lectures given at the C.I.M.E.-E.M.S. Summer School, held in Cetraro, Italy, July 1-10, 1999 (2005) (1)
On the problem of stability for near to integrable Hamiltonian systems (2012) (1)
Methods of complex analysis in classical perturbation theory (1995) (1)
Cosmic Visions in Celestial Mechanics (2010) (1)
Recent Results on the Fermi-Pasta-Ulam Problem (2005) (1)
From Kolmogorov’s Normalization Algorithm to the Orbits in the Three-Body Planetary Problem (2002) (1)
IMPROVED ESTIMATES FOR THE CONVERGENCE RADIUS IN THE POINCARÉ – (2015) (1)
Roger Joseph Boscovich between geometry and astronomy (2013) (0)
The effective Stability in the restricted Three Body Problem (1996) (0)
On a notion of weak stability and its relevance for celestial mechanics and molecular dynamics (1994) (0)
THE NONLINEAR SCHRÖDINGER EQUATION AS A RESONANT NORMAL FORM D. Bambusi and A. Carati (2001) (0)
Improved convergence estimates for the Schröder–Siegel problem (2014) (0)
A Series Expansion for the Time Autocorrelation of Dynamical Variables (2012) (0)
EFFECTIVE STABILITY FOR REALISTIC PHYSICAL SYSTEMS (2012) (0)
Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability in the light of Kolmogorov and Nekhoroshev theories (2017) (0)
Construction of the Normal Form for Elliptic Tori in Planetary Systems. Part I: Numerical Validation of the Semi-Analytic Algorithm (2010) (0)
CANONICAL PERTURBATION THEORY FOR NEARLY INTEGRABLE SYSTEMS Introduction to the canonical perturbation theory for nearly integrable systems (2006) (0)
Extensive Adiabatic Invariants for Nonlinear Chains (2012) (0)
Perturbation Methods in Celestial Mechanics (2019) (0)
A Tribute to Jürgen Moser (2000) (0)
ORDER, DISORDERAND PHASE TRANSITIONS IN QUANTUMMANY BODY SYSTEMS (2020) (0)
THE USE OF FOURIER TRANSFORM IN INTERPRETING VIBRATIONAL. SPECTRA. (1993) (0)
IMPROVED CONVERGENCE ESTIMATES FOR THE SCHRÖDER-SIEGEL (2013) (0)
Fractal dimensions and exponentially large time scales in conservative dynamical systems (1993) (0)

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Why Is Antonio Giorgilli Influential?

Antonio Giorgilli's Published Works

Published Works

Other Resources About Antonio Giorgilli

What Schools Are Affiliated With Antonio Giorgilli?

Antonio Giorgilli's AcademicInfluence.com Rankings